Question

Use the change of base formula to simplify log6aloga
log
6
⁡
𝑎
log
⁡
𝑎
.(1 point)
Responses

1loga
1
log
⁡
𝑎
Start Fraction 1 over logarithm a End Fraction

log6
log
⁡
6
logarithm 6

log610
log
6
⁡
10
logarithm subscript 6 baseline 10

1log6

Answer 1

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)