1. The problem asks if $\log(7/5)$ divided by $\log(3/4)$ is the same as $\lg(7/5)/\lg(3/4)$. 2. Here, $\lg$ typically denotes the logarithm base 10, and $\log$ without a base often means the natural logarithm (base $e$) or can also mean base 10 depending on context. 3. The change of base formula states: $$\log_a b = \frac{\log_c b}{\log_c a}$$ for any positive $a,b,c \neq 1$. 4. Using this, $\frac{\lg(7/5)}{\lg(3/4)}$ is the logarithm of $7/5$ base $3/4$. Similarly, $\frac{\log(7/5)}{\log(3/4)}$ is also the logarithm of $7/5$ base $3/4$ but using natural logs. 5. Since the ratio of logarithms with the same base is independent of the base chosen, both expressions are equal. 6. Therefore, $$\frac{\lg(7/5)}{\lg(3/4)} = \frac{\log(7/5)}{\log(3/4)}$$ This means the two expressions are the same value.