Answer
False
Work Step by Step
$\frac{\log_7x}{\log_7y}$ is equivalent to $\log_yx$.
When an expression in the form $\log_xa−\log_xb$ is given, it is a logarithm rule that it can be rewritten in in the form $\log_x\frac{a}{b}$, and vice versa.
Thus, $\log_7x−\log_7y$ can be rewritten as $\log_7\frac{x}{y}$ and
$\log_yx \ne \log_7\frac{x}{y}$
The statement is thus false.