Problem
Which of the following is equivalent to \( \frac{\log _{c}(6)}{\log (6)} \) ?
Solution
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: \( \frac{\log (6)}{\log _{c}(6)} \cdot \log _{c}(6) = \log (6) \)
