We are asked to simplify the expression $\frac{\log 125}{\log 25}$.

1. Problem Description

We are asked to simplify the expression $\frac{\log 125}{\log 25}$.

2. Solution Steps

We can rewrite 125 as $5^3$ and 25 as $5^2$. Therefore, the expression becomes $\frac{\log 5^3}{\log 5^2}$.

Using the logarithm power rule, $\log a^b = b \log a$, we can rewrite the expression as $\frac{3\log 5}{2\log 5}$.

We can cancel out the $\log 5$ terms in the numerator and the denominator, giving us $\frac{3}{2}$.

3. Final Answer

The simplified expression is $\frac{3}{2}$.