To simplify the expression \(\frac{\log_6 a}{\log a}\) using the change of base formula, we can rewrite the logarithms in terms of a common base, such as base 10 or base \(e\).
The change of base formula states that:
\[ \log_b a = \frac{\log_k a}{\log_k b} \]
Applying this to our case:
\[ \log_6 a = \frac{\log a}{\log 6} \]
Now substituting this into the original expression gives:
\[ \frac{\log_6 a}{\log a} = \frac{\frac{\log a}{\log 6}}{\log a} = \frac{1}{\log 6} \]
Based on the options provided, the correct simplified expression is:
\[ \frac{1}{\log 6} \]
Thus, the response is:
1
1 / log 6 (if this formatting is recognized based on the response option)
1 answer