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Rewrite the following in the form log(c). log(6)-log(2)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(6)−log⁡(2) \log (6)-\log (2)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(6)−log⁡(2) \log (6)-\log (2)
  1. Identify Property: Identify the property to simplify the expression log⁡(6)−log⁡(2)\log(6) - \log(2).\newlineThe difference of logarithms of two numbers equals the logarithm of their quotient.\newlineQuotient property: log⁡bP−log⁡bQ=log⁡b(P/Q)\log_b P - \log_b Q = \log_b (P/Q)
  2. Apply Quotient Property: Apply the quotient property of logarithms to log⁡(6)−log⁡(2)\log(6) - \log(2).log⁡(6)−log⁡(2)=log⁡(62)\log(6) - \log(2) = \log\left(\frac{6}{2}\right)
  3. Calculate Quotient: Calculate the quotient 6/26/2.\newline6/2=36/2 = 3
  4. Rewrite Expression: Rewrite the expression using the result from Step 33. log⁡(6)−log⁡(2)=log⁡(3)\log(6) - \log(2) = \log(3)

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