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<!-- Creation Date :2026-03-05T12:46:26.0246+00:00 -->
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive loss before reclassifications</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringReserve_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance at the beginning of the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringReserve_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance at the end of the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringReserve_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Reserve</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfRevolvingBorrowingsExceedOfTotalCommitments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of revolving borrowings exceed of total commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfRevolvingBorrowingsExceedOfTotalCommitments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of revolving borrowings exceed of total commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based compensation arrangement by share-based payment award, options, vested in period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Vested In Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Inputs, Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net of Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total deferred tax assets, net of valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowHedgingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Flow Hedging [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowHedgingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash Flow Hedges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Four Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche Three [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsCapitalLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Capital Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsCapitalLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Capital loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsCapitalLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax assets for capital losses increased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Temporary equity stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Termination Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee termination date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTerminationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Termination date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowances and Reserves Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SEC Schedule, 12-09, Valuation Allowances and Reserves Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of operating lease ROU assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon settlement of restricted stock units, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleReportToBoardFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible Report to Board [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskBoardOfDirectorsOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Board of Directors Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer Benchmark [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement by Share Based Payment Award Fair Value Assumptions Equity Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award fair value assumptions equity value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash, Noncurrent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Increase Resulting from Current Period Tax Positions</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, cash payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cumulative translation gain (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Costs of Goods Sold</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decrease in valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Decrease in valuation allowance of deferred tax asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockDividendSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock dividend shares issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockDividendSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock Dividend Shares Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockDividendSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred stock dividend shares issuable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Hedging Relationship</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Relationship [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expenses and Other Current Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskThirdPartyOversightAndIdentificationProcessesFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Third Party Oversight and Identification Processes [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRestructuringAndRelatedCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Severance and Other Personnel Reduction Liabilities Included Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRestructuringAndRelatedCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Costs [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxAssetsIncreaseOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred tax assets increase operating loss carryforwards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxAssetsIncreaseOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets Increase Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxAssetsIncreaseOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax assets NOL increased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal benefit at statutory rate, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Basis of presentation and consolidation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis Of Presentation And Consolidation Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation and Consolidation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss contingency number of cases dismissed by plaintiff.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency Number Of Cases Dismissed By Plaintiff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of cases dismissed by plaintiff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementThirdPartyEngagedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Third Party Engaged [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentsIncorporatedByReferenceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Documents Incorporated by Reference [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentsIncorporatedByReferenceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Documents Incorporated by Reference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInStockBasedCompensationExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in stock based compensation expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInStockBasedCompensationExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Stock Based Compensation Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInStockBasedCompensationExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decrease in stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total provision for income taxes, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common Stock Options Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes, net of refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Jurisdiction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Authority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnlimitedCarryoverPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unlimited carryover period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnlimitedCarryoverPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unlimited Carryover Period [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnlimitedCarryoverPeriodMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unlimited Carryover Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfIncomeTaxContingenciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Income Tax Contingencies [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfIncomeTaxContingenciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of Beginning and Ending Amount of Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographical</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash, Cash Equivalents and Restricted Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Refunds Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, refunds liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Refunds liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash lease expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Lease Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Original maturities of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property Plant And Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Disaggregation Of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computation of Basic and Diluted Net Loss Per Share Attributable to Common Stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesChargedToCostAndExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowances and Reserves, Additions, Charge to Cost and Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesChargedToCostAndExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesChargedToCostAndExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Valuation allowance increased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued distributions</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCovenantTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Covenant Terms</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Options, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Options, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Assets Of Disposal Group Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net assets of disposal group including discontinued operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest and other income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income (Expense), Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment of Leasehold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of leasehold improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Right-of-Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, right-of-use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Designation [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Hedging Designation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EntityWideRevenueMajorCustomerLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue, Major Customer [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EntityWideRevenueMajorCustomerLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue, Major Customer [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Changes in Estimated Fair Value of Level 3 Financial Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Domestic Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesDeductions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowances and Reserves, Deduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesDeductions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deductions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Funds Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, funds receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Increase Resulting from Prior Period Tax Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additions for tax positions of prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminatedPeriodPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Reduction In workforce, number of positions reduced, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminatedPeriodPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Cost, Number of Positions Eliminated, Period Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminatedPeriodPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restructuring plan, number of positions reduced, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders&#8217; equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Notional Amounts of Outstanding Derivative Positions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Total Gross Notional Amounts of Outstanding Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Designation [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingDesignationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Hedging Designation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net of Valuation Allowance [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNetOfValuationAllowanceAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographic Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographic Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of stock, price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Foreign Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current foreign tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentForeignTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Time-based Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Time-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Time-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ResearchAndDevelopmentExpensesCarryforwardAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Research and development expenses carryforward amortization period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ResearchAndDevelopmentExpensesCarryforwardAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expenses Carryforward Amortization Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ResearchAndDevelopmentExpensesCarryforwardAmortizationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development expenses carryforward amortization period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee Lease Description [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Abrams Capital Partners I LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ACP I</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Abrams capital partners I, LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contribution Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contribution Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contribution agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal benefit at statutory rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued and Unpaid Distributions Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and unpaid distributions per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued and unpaid distributions per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of subscription rights to purchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Chief Executive Officer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Chief Executive Officer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Net assets sold pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Net Assets Sold Pursuant To The Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation net assets sold pursuant to the asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities, Redeemable Non-controlling Interest, and Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2020 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationMinorityInterestIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Noncontrolling Interest Income (Loss), Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationMinorityInterestIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseRestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Restructuring Charges, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseRestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Severance paid by Qoo10</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskRoleOfManagementTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Role of Management [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingRelationshipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Relationship [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingRelationshipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Hedging Relationship</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Fair Value of Derivative Financial Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EscrowDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Escrow fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EscrowDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Escrow Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss contingency number of cases coordinated and consolidated.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency Number Of Cases Coordinated and Consolidated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of cases coordinated and consolidated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total gross deferred tax liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Liabilities, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Valuation Assumptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Currency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrJunYanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Mr. Jun Yan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrJunYanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mr. Jun Yan[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrJunYanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mr. Jun Yan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Units Issuable For Future Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional units issuable for future investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional units issuable for future investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Derivative Asset, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Balance Sheet Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">ROU assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total gross deferred tax assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseOfTaxCreditLimiationPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Of Tax Credit Limiation Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseOfTaxCreditLimiationPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase of tax credit limiation percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseOfTaxCreditLimiationPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase of tax credit limitation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskProcessForInformingBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Process for Informing Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rights Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rights offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rights Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event Type</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRefundLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Refund Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRefundLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Refunds liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other comprehensive income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Later of Two Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Base Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Alternative Base Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current and noncurrent liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Abrams Capital Partners II LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ACP II</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Abrams capital partners II, LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxLiabilitiesPropertyAndEquipmentIncludingRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred tax liabilities property and equipment including right of use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxLiabilitiesPropertyAndEquipmentIncludingRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities Property And Equipment Including Right Of Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxLiabilitiesPropertyAndEquipmentIncludingRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Property and equipment, including right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFinStmtErrorCorrectionFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Financial Statement Error Correction [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon exercise of options, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Elements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental cash flow disclosures:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total gross notional amounts of outstanding derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty two inducement plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Two Inducement Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2022 Inducement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsReceivedFromBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds received from backstop agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsReceivedFromBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Proceeds Received From Backstop Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsReceivedFromBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gross proceeds received from backstop agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanAndSeriesAJuniorParticipatingPreferredStockPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Benefits Preservation Plan and Series A Junior Participating Preferred Stock [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanAndSeriesAJuniorParticipatingPreferredStockPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax Benefits Preservation Plan and Series A Junior Participating Preferred Stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanAndSeriesAJuniorParticipatingPreferredStockPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Benefits Preservation Plan and Series A Junior Participating Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advertising Cost [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Advertising Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Restricted Stock Units, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Restricted Stock Units, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity awards outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested share outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InternalUseSoftwarePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Internal Use Software, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InternalUseSoftwarePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Software Development Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RachelWangMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rachel Wang [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RachelWangMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rachel Wang.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RachelWangMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rachel Wang</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Liabilities Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total financial liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive loss attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographical</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrVijayTalwarMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Mr. Vijay Talwar</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrVijayTalwarMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mr. Vijay Talwar[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MrVijayTalwarMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mr. Vijay Talwar</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of stock, shares converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of shares exchanged for each share of Class A common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Cash Adjustment Pursuant To The Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation cash adjustment pursuant to the asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Cash adjustment pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseRestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Restructuring Charges, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseRestructuringCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Severance paid by Qoo10, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State tax (benefit), net of federal benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock-Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Salt Holdings LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US salt holdings, LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Salt Holdings, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Deferred Tax Assets and Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Merchants Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, merchants payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Merchants payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">PSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance-Based Units ("PSUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Redeemable noncontrolling interest disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Non-controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfCashFlowInformationForOperatingLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of cash flow information for operating leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfCashFlowInformationForOperatingLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Cash Flow Information For Operating Leases Table [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfCashFlowInformationForOperatingLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental Cash Flow Information for Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of redeemable convertible Preferred Units, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Merchants payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Merchants Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Merchants payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Other Comprehensive Income Loss Cash Flow Hedge Gain Loss After Reclassification</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance at the end of the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance at the beginning of the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unrealized other comprehensive income loss cash flow hedge gain loss after reclassification.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty two employee stock purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Two Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyTwoEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2022 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StateAndLocalJurisdictionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">State and Local Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StateAndLocalJurisdictionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinimumNetWorthRequiredForCompliance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Banking Regulation, Mortgage Banking, Net Worth, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinimumNetWorthRequiredForCompliance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum liquidity financial covenant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Derivative Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, purchase price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Preferred, Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted initial carrying value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.0001 par value: 100,000 shares authorized as of December 31, 2025 and 2024; No shares issued and outstanding as of December 31, 2025 and 2024</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Discontinued Operations of Asset Held for Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average grant date fair value, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-Average Grant Date Fair Value, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExecutiveChairMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Executive Chair.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExecutiveChairMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Executive Chair [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExecutiveChairMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Executive Chair</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Each Warrant or Right</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of each subscription rights to purchase shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class B [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Class B Common Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Fair Value Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Financial Assets and Liabilities Subject to Fair Value Measurements on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Period [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restructuring Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, additional borrowing capacity.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility Additional Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Loss Carryforwards</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Accrued Liabilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowances and Reserves [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SEC Schedule, 12-09, Valuation Allowances and Reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted-Average Grant Date Fair Value, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted-Average Grant Date Fair Value, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock and Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentAndTerminationRelatedCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Impairment and termination related charges.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentAndTerminationRelatedCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment And Termination Related Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentAndTerminationRelatedCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment and termination related charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and Administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfFinanceLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of finance leases outstanding.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfFinanceLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Finance Leases Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfFinanceLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of finance leases outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Lease, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorFirmId_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Firm ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorFirmId_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Auditor Firm ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving credit facility, variable interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LogisticsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Logistics.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LogisticsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Logistics [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LogisticsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Logistics Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary Of Significant Accounting Policies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Benchmark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecuritiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">600K Class P Unit Award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">600K Class P Unit Award [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">600K class P unit award.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee Lease Description [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in federal valuation allowance, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Foreign currency effects on cash, cash equivalents, and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency effects on cash, cash equivalents, and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCollateralForBorrowedSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Collateral for Borrowed Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCollateralForBorrowedSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash collateral received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Operating Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Add: Transaction costs paid by buyer on behalf of the Company at closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty employee stock purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTwentyEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2020 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Transaction Costs Incurred in Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Estimated transaction costs incurred in expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average shares used in computing net loss per share attributable to common stockholders, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in merchants payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Merchants Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Merchants payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from External Customers by Geographic Areas [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Revenue by Geographic Area</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based compensation arrangements by share-based payment award, options, vested in period, weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Options Vested In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtSecuritiesAvailableForSaleContractualMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt securities available for sale contractual maturity.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtSecuritiesAvailableForSaleContractualMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities Available For Sale Contractual Maturity Table [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtSecuritiesAvailableForSaleContractualMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Contractual Maturities of Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee stock purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">ESPP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of Income Taxes Computed at Statutory Federal Income Tax Rate and Provision for Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Asset, In-Process Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred tax asset recognized net impact of capitalization of research and development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsInProcessResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalization of research and development expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in federal valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders&#8217; equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand ten equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Ten Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TwoThousandTenEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2010 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestByLegalEntityTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Later of Three Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Goods and Service [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNonvestedShareActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Nonvested Share Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNonvestedShareActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Non-vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary Of Significant Accounting Policies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold Improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net loss attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Net loss attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling and Marketing Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales and Marketing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedIncomeStatementTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Total Severance and Other Personnel Reduction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScheduleOfCondensedIncomeStatementTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Condensed Income Statement [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial Instruments and Fair Value Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInAccruedAndRefundLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in accrued and refund liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInAccruedAndRefundLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Accrued And Refund Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInAccruedAndRefundLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and refund liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options grant date fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted stock units, granted date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/label">UNITED STATES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">United States</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase in Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in operating loss carryforwards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, Date of Incorporation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity incorporation, date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation, Foreign Currency Translation Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derecognition of accumulated currency translation on asset sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Unrecognized Tax Benefits Roll Forward [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of acquiring Beneficial ownership.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of acquiring Beneficial ownership.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of acquiring beneficial ownership</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardEmployeeStockPurchasePlanValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Employee Stock Purchase Plan, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardEmployeeStockPurchasePlanValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Assumptions Used in Black-Scholes Option Pricing Model</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance, beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Including Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Temporary Equity, Including Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance, end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FurnitureAndFixturesServersAndNetworkingEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Furniture and fixtures, servers and networking equipment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FurnitureAndFixturesServersAndNetworkingEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture And Fixtures Servers And Networking Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FurnitureAndFixturesServersAndNetworkingEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and Fixtures, Servers, Networking Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reference Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reference Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reference Rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current State and Local Tax Expense (Benefit)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current state tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current state tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Description and Basis of Presentation [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessDescriptionAndBasisOfPresentationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Description of Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementExpertiseOfManagementResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Expertise of Management Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate number of rights to purchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Period [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A Convertible Preferred Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class A convertible preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Convertible Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockDividendPayableRecordDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Dividend Payable Record Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockDividendPayableRecordDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock dividend payable record date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockDividendPayableRecordDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend record date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Other Adjustments, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdateExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Benefits Preservation Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Benefits Preservation Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxBenefitsPreservationPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax benefits preservation plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_EuropeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Europe [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_EuropeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Europe</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Variable Interest Rate, Type [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Redeemable Noncontrolling Interest, Equity, Carrying Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other adjustments, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Loss before provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss before provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vest upon the performance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term loan facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Cash Flow Hedges Included in Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Changes in Accumulated Other Comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities, Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign rate differential, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsWorthOfPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Restricted Stock Units Worth</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsWorthOfPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Worth of Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsWorthOfPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options worth of period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment service providers, two.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment Service Providers Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PSP 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGoodwillAndIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGoodwillAndIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Goodwill and Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash, cash equivalents and restricted cash at end of year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash, cash equivalents and restricted cash at beginning of year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash, cash equivalents and restricted cash at beginning of year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price of rights per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of Individual</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_IcfrAuditorAttestationFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ICFR Auditor Attestation Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_IcfrAuditorAttestationFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ICFR Auditor Attestation Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitment fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease, liability current, Statement of financial position [Extensible List]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested Restricted Stock Units Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units ("RSUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MarketplaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Marketplace [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MarketplaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketplace [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MarketplaceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketplace Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AssetsAndLiabilitiesHeldForSalePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets and Liabilities Held for Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AssetsAndLiabilitiesHeldForSalePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets And Liabilities Held for sale [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AssetsAndLiabilitiesHeldForSalePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Assets And Liabilities Held for sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Aggregate Enterprise Value of Acquisition of Businesses or Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Aggregate Enterprise Value of Acquisition of Businesses or Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Antidilutive Securities Excluded From Computation Of Earnings Per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income :</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of cash, cash equivalents, and restricted cash to the consolidated balance sheets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncentivePlanApprovalDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Incentive plan approval date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncentivePlanApprovalDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Incentive Plan Approval Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncentivePlanApprovalDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incentive plan approval date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash paid for amounts included in measurement of lease liabilities..</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Paid For Amounts Included In Measurement Of Lease Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for amounts included in the measurement of lease liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ValuationAndQualifyingAccountsDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Valuation And Qualifying Accounts Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ValuationAndQualifyingAccountsDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NondesignatedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Not Designated as Hedging Instrument [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NondesignatedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-designated Hedges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Values Derivatives Balance Sheet Location By Derivative Contract Type By Hedging Designation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses, Net of Cash Divested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash disposed on Asset Sale, net of proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award requisite service period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign rate differential</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCash_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Restricted Cash, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advertising Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvertisingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Advertising expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignExchangeForwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Exchange Forward [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignExchangeForwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Exchange Forward Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesBalance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowances and Reserves, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesBalance_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance at End of Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowancesAndReservesBalance_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance at Beginning of Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized holding losses on derivatives and marketable securities, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other comprehensive income unrealized holding gain loss on derivatives and marketable securities arising during period net of tax.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income Unrealized Holding Gain Loss On Derivatives And Marketable Securities Arising During Period Net Of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing net loss per share attributable to common stockholders, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Reduced Principal Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, reduced principal amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reduced revolving credit facility aggregate principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cover</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExercisePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExercisePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exercise Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExercisePricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Exercise price per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Restricted Stock Units, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfValuationAllowanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Valuation Allowance [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfValuationAllowanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Deferred Tax Asset Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">U.S. Treasury Bills</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentOfTaxesRelatedToRSUSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of taxes related to RSU settlement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentOfTaxesRelatedToRSUSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment Of Taxes Related To R S U Settlement</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ValuationAndQualifyingAccountsDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ValuationAndQualifyingAccountsDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Valuation And Qualifying Accounts Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnForeignCurrencyDerivativeInstrumentsNotDesignatedAsHedgingInstruments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Foreign Currency Derivative Instruments Not Designated as Hedging Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnForeignCurrencyDerivativeInstrumentsNotDesignatedAsHedgingInstruments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net gains (losses) on change in fair value of foreign exchange forward contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares awarded as compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherCountriesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other Countries.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherCountriesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Countries [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherCountriesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Value Of Additional Units Issuable For Future Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Value of additional units issuable for future investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Value of additional units issuable for future investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average exercise price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discount for lack of marketability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Fair Value Assumptions Discount For Lack Of Marketability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award fair value assumptions discount for lack of marketability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative contract term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated useful lives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturities of Operating Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award options grant date fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantDateFairValue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options, Grant date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award service condition satisfaction period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net borrowing proceeds from initial term loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease, liabilities current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net deferred tax assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Property, Plant and Equipment, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Non-Controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost of Revenue, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_NoTradingSymbolFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">No Trading Symbol Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Components of Income Tax Expense (Benefit) [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Provision for Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Federal Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations and Disposal Groups [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value of options outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeAmountsAttributableToNoncontrollingInterestDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Amounts Attributable to Noncontrolling Interest, Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Dividends and Accretion to Adjust Redemption Value of Subsidiary's Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued dividends and accretion to adjust redemption value of subsidiary's preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued distributions and accretion to adjust redemption value of subsidiary's preferred units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Convertible, Shares Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred shares issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Share-Based Arrangements, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensation expense to be recognized related to vesting of award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend yield</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase obligation for asset sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Purchase Obligation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesFairValueLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivatives, Fair Value [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesFairValueLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivatives Fair Value [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Senior secured debt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Senior Secured Debt [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior Secured Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses, other current and noncurrent assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Issuance of Subsidiary to Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity issuance of subsidiary to noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of subsidiary's Preferred Units to redeemable non-controlling interest, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration Risk Benchmark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employment agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock Consideration Receivable on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock consideration receivable on transaction.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate purchase price receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested in Period, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate fair value of options vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Components of Loss Before Provision for Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Preferred, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mezzanine equity and initially recognized at fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Excluded Cash At Closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation excluded cash at closing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Excluded cash at closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Noncontrolling Interest Component of the Company's Condensed Consolidated Statements of Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of Noncontrolling Interest Component of the Company's Condensed Consolidated Statements of Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Noncontrolling Interest Component of Company's Consolidated Statements of Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain on asset sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Federal Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest, Decrease from Redemptions or Purchase of Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reduced cost of issuing value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossAndAdjustmentAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Loss and Adjustment Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossAndAdjustmentAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net loss and adjustment attributable to redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossAndAdjustmentAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss and adjustment attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCostAndReserveLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Cost and Reserve [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Measurement, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">BCP Special Opportunities Fund III Originations LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">BCP Special Opportunities Fund III Originations LP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">BCP Special Opportunities Fund III Originations LP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">BCP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NorthAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">North America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NorthAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">North America</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAndRentalExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Leases, Rent Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseAndRentalExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating leases, rent expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Consideration Received on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate purchase amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities held-for-sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Redeemable Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net loss attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Instrument</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized compensation expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total financial assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivatives, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of funds receivable balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-lived tangible assets percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance-based Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Performance-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Conversion of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationMinorityInterestIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Noncontrolling Interest Income (Loss), Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationMinorityInterestIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Redeemable non-controlling interest, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationMinorityInterestIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Funds receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Funds Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock-based compensation increase (decrease) in provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative Financial Instruments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Grant Date Fair Value, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money Market Funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other liabilities, non-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted-Average Exercise Price, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted-Average Exercise Price, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance at December 31</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance at January 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Adoption Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due within one year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrestrictedCashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrestricted cash, cash equivalents, and marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrestrictedCashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrestricted Cash, Cash Equivalents, And Marketable Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnrestrictedCashCashEquivalentsAndMarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unrestricted cash, cash equivalents, and marketable securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock Purchase Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock Purchase Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred stock purchase rights.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Prepaid and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee payables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitment fee percentage on unused portion of aggregate commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income taxes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Expected time to a liquidity event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment service providers, one.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment Service Providers One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentServiceProvidersOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PSP 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentsOfLeaseAssetsAndPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Impairments of lease assets and property and equipment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentsOfLeaseAssetsAndPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairments Of Lease Assets And Property And Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ImpairmentsOfLeaseAssetsAndPropertyAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairments of lease assets and property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Research and development credits, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling and Marketing Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales and marketing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling and Marketing Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Components</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Activity Under Equity Plans and Related Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Merchants payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Merchants Payable Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MerchantsPayablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Merchants Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">SEC Schedule, 12-09, Valuation Allowance, Deferred Tax Asset [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Valuation Allowance of Deferred Tax Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">IPO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award, expiration period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term of option award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationAmountOfContinuingCashFlowsAfterDisposal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment to Qoo10</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationAmountOfContinuingCashFlowsAfterDisposal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Amount of Continuing Cash Flows after Disposal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DesignatedAsHedgingInstrumentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Designated as Hedging Instrument [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DesignatedAsHedgingInstrumentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Designated Hedges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.0001 par value: 3,000,000 shares authorized as of December 31, 2025 and 2024; 26,876 and 26,229 shares issued and outstanding as of December 31, 2025 and 2024, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Annual Percentage of Distribution Accrued on Consummation of Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity annual percentage of distribution accrued on consummation of acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual percentage of distribution accrued on consummation of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Agggregate purchase of rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants and Rights Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate (SOFR) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Secured Overnight Financing Rate ("SOFR")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Assets, Operating Loss Carryforwards, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">NOL carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesForAssessingIdentifyingAndManagingThreatsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes for Assessing, Identifying, and Managing Threats [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationCommonStockSharesOutstandingPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation common stock shares outstanding percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationCommonStockSharesOutstandingPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Common Stock Shares Outstanding Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationCommonStockSharesOutstandingPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock shares outstanding percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of Long-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State tax (benefit), net of federal benefit, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock price volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: comprehensive loss attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: comprehensive loss attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Restricted stock units and stock options.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units and Stock Options [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units (RSUs) and Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Accretion to Redemption Value, Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: adjustments attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: adjustments attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Adjustments attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Accelerated Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense upon acceleration of Class P units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Additional Paid in Capital, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred State and Local Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfOperatingLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Operating Leases Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfOperatingLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of operating leases outstanding.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfOperatingLeasesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating leases outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PropertyPlantAndEquipmentEstimatedUsefulLivesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Property, plant and equipment, estimated useful lives.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PropertyPlantAndEquipmentEstimatedUsefulLivesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property Plant And Equipment Estimated Useful Lives Table [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PropertyPlantAndEquipmentEstimatedUsefulLivesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated Useful Lives of Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds from subscribers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income taxes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of ownership of holdings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration of Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensation Related Costs, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandTwentySixThroughTwoThousandFortyFiveMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Period Begin To Expire In Two Thousand Twenty Six Through Two Thousand Forty Five [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandTwentySixThroughTwoThousandFortyFiveMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax Period Begin To Expire In Two Thousand Twenty Six Through Two Thousand Forty Five.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandTwentySixThroughTwoThousandFortyFiveMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Period begin to expire in 2026 through 2045</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRestructuring_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cash payments during the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRestructuring_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash payments during the period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRestructuring_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Restructuring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationDispositionOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Disposition of Asset, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationDispositionOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis difference on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Restricted Stock Units, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested share outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, by Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Property Plant And Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RatioOfIndebtednessToNetCapital1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ratio of Indebtedness to Net Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RatioOfIndebtednessToNetCapital1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum ratio of aggregate principal amount of third party indebtedness to consolidated EBITDA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRestructuringAndRelatedCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Cost [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Decrease Resulting from Prior Period Tax Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Decreases for tax positions of prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromPriorPeriodTaxPositions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Decreases for tax positions of prior years</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value of RSUs outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Deferred income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total deferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total deferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Number of Shares Issued in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued and sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Sale of stock, number of shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProductBoostMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ProductBoost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProductBoostMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Boost [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProductBoostMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ProductBoost Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign exchange-related adjustment included in Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign-Exchange Related Adjustment Included in Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other comprehensive income (loss),foreign-exchange related adjustment included in asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Restricted Stock Units, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12gTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(g) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of Individual</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of putative class action lawsuits,</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Putative Class Action Lawsuits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of putative class action lawsuits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLifeDescriptionOfTermExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated useful lives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLifeDescriptionOfTermExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets held-for-sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Auditor Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cumulative Fair Value Of Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cumulative fair value of grant.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cumulative fair value of grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Debt instrument, aggregate principal amount</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan Facility, principal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior secured revolving credit facility</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Research and development credits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, standby letter of credit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility Standby Letter Of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Standby letter of credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Amounts recognized in core marketplace revenue and reclassified out of accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherDirectorOrOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Director or Officer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherDirectorOrOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other director or officer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherDirectorOrOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Director or Officer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEntityWideRevenueByMajorCustomersByReportingSegmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Revenue by Major Customers, by Reporting Segments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEntityWideRevenueByMajorCustomersByReportingSegmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Entity Wide Revenue By Major Customers By Reporting Segments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueVested_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueVested_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average remaining lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandThirtyThroughTwoThousandThirtySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax period begin to expire in two thousand thirty through two thousand thirty seven.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandThirtyThroughTwoThousandThirtySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Period Begin To Expire In Two Thousand Thirty Through Two Thousand Thirty Seven [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxPeriodBeginToExpireInTwoThousandThirtyThroughTwoThousandThirtySevenMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Period begin to expire in 2030 through 2037</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options exercisable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Restricted Stock Units, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letters of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, equity rollover condiseration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred foreign tax expense (benefit)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Reconciliation Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income tax reconciliation transaction costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeTaxReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Condensed consolidated statements of operations</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Reduction in workforce, number of positions reduced</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Cost, Number of Positions Eliminated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restructuring plan, number of positions reduced</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ComputersEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Computers, equipment and software.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ComputersEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computers, Equipment, Software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpectedProceedsFromRightsOfferingAndBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Expected Proceeds From Rights Offering And Backstop Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpectedProceedsFromRightsOfferingAndBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected proceeds from rights offering and backstop agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpectedProceedsFromRightsOfferingAndBackstopAgreements_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Expected proceeds from rights offering and backstop agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average discount rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class Of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Table Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorLocation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Location</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BalanceSheetComponentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Balance sheet components.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis difference on Asset Sale, percent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Jurisdiction [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Authority</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Gross [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Funds receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Funds Receivable Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivablePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Lines of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash collateral released</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual percentage of distribution accrued until consummation of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Annual Percentage of Distribution accrued until Consummation of Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity annual percentage of distribution accrued until consummation of acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation transaction costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedules of Concentration of Risk, by Risk Factor [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of PSPs Each Represented 10% or More of Funds Receivable Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">common stock per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Axis]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Term</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxesNetOfFederalTaxBenefitPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State tax (benefit), net of federal benefit, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxesNetOfFederalTaxBenefitPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, State and Local Income Taxes Net of Federal Tax Benefit Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxesNetOfFederalTaxBenefitPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation, state and local income taxes net of federal tax benefit percent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Maturities, Prepayments and Calls of Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturities of marketable securities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Short-Term Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term lease costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_CN_lbl" xlink:role="http://www.xbrl.org/2003/role/label">CHINA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_CN_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">China</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorOpinionTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Opinion [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Numerator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CostOfRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of Revenue [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CostOfRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost Of Revenue [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CostOfRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares available for grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized compensation expenses, recognition period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Professional Fees, Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Funds receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Funds Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
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  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability" name="DisposalGroupIncludingDiscontinuedOperationRefundsLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_DeferredTaxLiabilitiesPropertyAndEquipmentIncludingRightOfUseAssets" name="DeferredTaxLiabilitiesPropertyAndEquipmentIncludingRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_TwoThousandTwentyTwoInducementPlanMember" name="TwoThousandTwentyTwoInducementPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DeferredTaxAssetsIncreaseOperatingLossCarryforwards" name="DeferredTaxAssetsIncreaseOperatingLossCarryforwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_AbramsCapitalPartnersILPMember" name="AbramsCapitalPartnersILPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition" name="TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PropertyPlantAndEquipmentEstimatedUsefulLivesTableTextBlock" name="PropertyPlantAndEquipmentEstimatedUsefulLivesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxesNetOfFederalTaxBenefitPercent" name="EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxesNetOfFederalTaxBenefitPercent" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PaymentOfTaxesRelatedToRSUSettlement" name="PaymentOfTaxesRelatedToRSUSettlement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_PercentageOfRevolvingBorrowingsExceedOfTotalCommitments" name="PercentageOfRevolvingBorrowingsExceedOfTotalCommitments" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_PercentageOfCashAndCashEquivalentsHeld" name="PercentageOfCashAndCashEquivalentsHeld" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_IncreaseOfTaxCreditLimiationPercentage" name="IncreaseOfTaxCreditLimiationPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SeniorSecuredDebtMember" name="SeniorSecuredDebtMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_MrJunYanMember" name="MrJunYanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NumberOfFinanceLeasesOutstanding" name="NumberOfFinanceLeasesOutstanding" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_TwoThousandTwentyEmployeeStockPurchasePlanMember" name="TwoThousandTwentyEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TermLoanFacilityMember" name="TermLoanFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets" name="DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ExecutiveChairMember" name="ExecutiveChairMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_MerchantsPayablePolicyTextBlock" name="MerchantsPayablePolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ProductBoostMember" name="ProductBoostMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SaleOfStockConsiderationReceivableOnTransaction" name="SaleOfStockConsiderationReceivableOnTransaction" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition" name="TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PaymentServiceProvidersTwoMember" name="PaymentServiceProvidersTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale" name="OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_CreditAgreementMember" name="CreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated" name="LossContingencyNumberOfCasesCoordinatedAndConsolidated" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TaxPeriodBeginToExpireInTwoThousandTwentySixThroughTwoThousandFortyFiveMember" name="TaxPeriodBeginToExpireInTwoThousandTwentySixThroughTwoThousandFortyFiveMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TwoThousandTwentyEquityIncentivePlanMember" name="TwoThousandTwentyEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CommitmentsAndContingenciesDisclosureTable" name="CommitmentsAndContingenciesDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_UnrestrictedCashCashEquivalentsAndMarketableSecurities" name="UnrestrictedCashCashEquivalentsAndMarketableSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_RightsOfferingMember" name="RightsOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_FundsReceivable" name="FundsReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_MarketplaceMember" name="MarketplaceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_IncomeTaxReconciliationTransactionCosts" name="IncomeTaxReconciliationTransactionCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember" name="BCPSpecialOpportunitiesFundIIIOriginationsLPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CoreMarketplaceMember" name="CoreMarketplaceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable" name="DisposalGroupIncludingDiscontinuedOperationFundsReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_CommitmentsAndContingenciesDisclosureLineItems" name="CommitmentsAndContingenciesDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EffectiveIncomeTaxRateReconciliationBasisDifferenceOnAssetSale" name="EffectiveIncomeTaxRateReconciliationBasisDifferenceOnAssetSale" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing" name="DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_TwoThousandTwentyTwoEmployeeStockPurchasePlanMember" name="TwoThousandTwentyTwoEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" name="IncomeLossAttributableToRedeemableNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_LineOfCreditFacilityAdditionalBorrowingCapacity" name="LineOfCreditFacilityAdditionalBorrowingCapacity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_RedeemableNoncontrollingInterestPolicyTextBlock" name="RedeemableNoncontrollingInterestPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TaxBenefitsPreservationPlanMember" name="TaxBenefitsPreservationPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsWorthOfPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsWorthOfPeriod" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_OtherDirectorOrOfficerMember" name="OtherDirectorOrOfficerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NumberOfPutativeClassActionLawsuits" name="NumberOfPutativeClassActionLawsuits" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SharesWithheldRelatedToNetShareSettlementShares" name="SharesWithheldRelatedToNetShareSettlementShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PreferredStockPurchaseRightsMember" name="PreferredStockPurchaseRightsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SummaryOfSignificantAccountingPoliciesLineItems" name="SummaryOfSignificantAccountingPoliciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EstimatedTransactionCostsIncurredInExpenses" name="EstimatedTransactionCostsIncurredInExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ImpairmentsOfLeaseAssetsAndPropertyAndEquipment" name="ImpairmentsOfLeaseAssetsAndPropertyAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_LineOfCreditFacilityStandbyLetterOfCredit" name="LineOfCreditFacilityStandbyLetterOfCredit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation" name="NetAssetsOfDisposalGroupIncludingDiscontinuedOperation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_InvestmentAgreementMember" name="InvestmentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_IncreaseDecreaseInStockBasedCompensationExpenses" name="IncreaseDecreaseInStockBasedCompensationExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_NumberOfOperatingLeasesOutstanding" name="NumberOfOperatingLeasesOutstanding" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_TaxPeriodBeginToExpireInTwoThousandThirtyThroughTwoThousandThirtySevenMember" name="TaxPeriodBeginToExpireInTwoThousandThirtyThroughTwoThousandThirtySevenMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ImpairmentAndTerminationRelatedCharges" name="ImpairmentAndTerminationRelatedCharges" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_EmploymentAgreementMember" name="EmploymentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests" name="TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_BasisOfPresentationAndConsolidationPolicyTextBlock" name="BasisOfPresentationAndConsolidationPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SummaryOfSignificantAccountingPoliciesTable" name="SummaryOfSignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AbramsCapitalPartnersIILPMember" name="AbramsCapitalPartnersIILPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ComputersEquipmentAndSoftwareMember" name="ComputersEquipmentAndSoftwareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_MrVijayTalwarMember" name="MrVijayTalwarMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NoncashLeaseExpense" name="NoncashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_FundsReceivablePolicyTextBlock" name="FundsReceivablePolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_AdditionalUnitsIssuableForFutureInvestment" name="AdditionalUnitsIssuableForFutureInvestment" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PercentageOfAcquiringBeneficialOwnership" name="PercentageOfAcquiringBeneficialOwnership" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification" name="UnrealizedOtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassification" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_IncomeTaxesTable" name="IncomeTaxesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ExercisePricePerShare" name="ExercisePricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_LossContingencyNumberOfCasesDismissedByPlaintiff" name="LossContingencyNumberOfCasesDismissedByPlaintiff" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_Performance-BasedClassPUnitsMember" name="Performance-BasedClassPUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale" name="DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" name="CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_MerchantsPayable" name="MerchantsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ClassAConvertiblePreferredUnitsMember" name="ClassAConvertiblePreferredUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_IncomeTaxesLineItems" name="IncomeTaxesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
