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Rewrite the following in the form log(c). log(6)-log(3)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(6)−log⁡(3) \log (6)-\log (3)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(6)−log⁡(3) \log (6)-\log (3)
  1. Logarithm Property: log⁡(6)−log⁡(3)\log(6) - \log(3)\newlineWhich property can be used to simplify the expression?\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⁡(6)−log⁡(3)\log(6) - \log(3)\newlineApply the quotient property of logarithms.\newlinelog⁡(6)−log⁡(3)=log⁡(63)\log(6) - \log(3) = \log\left(\frac{6}{3}\right)
  3. Calculate Quotient: Calculate 6/36/3.\newline6/3=26/3 = 2
  4. Rewrite Expression: Rewrite the expression using the result from Step 33. log⁡(63)=log⁡(2)\log\left(\frac{6}{3}\right) = \log(2)

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