Simplify the expression $\frac{\log_{10} 125}{\log_{10} 25}$.

1. Problem Description

Simplify the expression $\frac{\log_{10} 125}{\log_{10} 25}$.

2. Solution Steps

We want to simplify the expression $\frac{\log_{10} 125}{\log_{10} 25}$.

We can rewrite $125$ as $5^3$ and $25$ as $5^2$. Therefore, the expression becomes

$\frac{\log_{10} 5^3}{\log_{10} 5^2}$.

Using the logarithm property $\log_b(a^c) = c \log_b a$, we have

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

Since $\log_{10} 5$ is a non-zero value, we can cancel $\log_{10} 5$ from the numerator and the denominator.

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

3. Final Answer

3/2