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Rewrite the following in the form log(c). log(8)-log(2)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(8)−log⁡(2) \log (8)-\log (2)

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Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(8)−log⁡(2) \log (8)-\log (2)
  1. Identify Property: log⁡(8)−log⁡(2)\log(8) - \log(2)\newlineIdentify the property that can be used to combine the logarithms.\newlineDifference of logarithms of two numbers equals the logarithm of their quotient.\newlineQuotient property: log⁡bP−log⁡bQ=log⁡b(PQ)\log_b P - \log_b Q = \log_b \left(\frac{P}{Q}\right)
  2. Apply Quotient Property: log⁡(8)−log⁡(2) \log(8) - \log(2) \newlineApply the quotient property of logarithms.\newlinelog⁡(8)−log⁡(2)=log⁡(82) \log(8) - \log(2) = \log\left(\frac{8}{2}\right)
  3. Calculate Division: Calculate 8/28/2.\newlineDivide 88 by 22 to get 44.\newlineextlog(8/2)=extlog(4) ext{log}(8/2) = ext{log}(4)
  4. Rewrite in Form: Rewrite log⁡(4)\log(4) in the form log⁡(c)\log(c).\newlineSince 44 is already a constant, we can express it as cc.\newlinelog⁡(4)=log⁡(c)\log(4) = \log(c) where c=4c = 4

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