1. The problem is to determine if a certain expression is equivalent to $\frac{\log 5}{\log 4}$. 2. Recall the change of base formula for logarithms: $$\log_a b = \frac{\log_c b}{\log_c a}$$ where $a$, $b$, and $c$ are positive numbers and $a \neq 1$, $c \neq 1$. 3. Using this formula, $\frac{\log 5}{\log 4}$ can be interpreted as $\log_4 5$. 4. Therefore, $\frac{\log 5}{\log 4}$ is equivalent to the logarithm of 5 with base 4. 5. In plain language, dividing the logarithm of 5 by the logarithm of 4 (both in the same base) gives you the logarithm of 5 in base 4. 6. So yes, $\frac{\log 5}{\log 4}$ is equivalent to $\log_4 5$.