Problem

Which of the following is equivalent to \( \frac{\log _{c}(6)}{\log (6)} \) ?

Answer

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Answer

Step 2: Simplify the expression: \( \frac{\log (6)}{\log _{c}(6)} \cdot \log _{c}(6) = \log (6) \)

Steps

Step 1 ：Step 1: Apply Change of Base Formula: \( \frac{\log _{c}(6)}{\log (6)} = \frac{\log (6)}{\log _{c}(6)} \cdot \frac{\log _{c}(6)}{\log (6)} = \frac{\log (6)}{\log _{c}(6)} \cdot \log _{c}(6) \)

Step 2 ：Step 2: Simplify the expression: \( \frac{\log (6)}{\log _{c}(6)} \cdot \log _{c}(6) = \log (6) \)

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