The problem asks to simplify the expression $\frac{\log_{10} 125}{\log_{10} 25}$.

1. Problem Description

The problem asks to simplify the expression $\frac{\log_{10} 125}{\log_{10} 25}$.

2. Solution Steps

We can rewrite 125 as $5^3$ and 25 as $5^2$. Thus, we have:

$\log_{10} 125 = \log_{10} 5^3 = 3 \log_{10} 5$

$\log_{10} 25 = \log_{10} 5^2 = 2 \log_{10} 5$

The expression then becomes:

$\frac{\log_{10} 125}{\log_{10} 25} = \frac{3 \log_{10} 5}{2 \log_{10} 5}$

Since $\log_{10} 5 \neq 0$, we can cancel out the $\log_{10} 5$ terms.

$\frac{3 \log_{10} 5}{2 \log_{10} 5} = \frac{3}{2}$

3. Final Answer

3/2