Answer
$\log_7{\left(\dfrac{32}{y^2}\right)}$
Work Step by Step
Recall:
(1) $n \cdot \log_a{b} = \log_a{\left(b^n\right)}$
(2) $\log_a{b}+\log_a{c}=\log_a{(bc)}$
(3) $\log_a{b} - \log_a{c}=\log_a{\left(\frac{b}{c}\right)}$
Use rule (1) above to obtain:
\begin{align*}
5\log_7{2}-2\log_7{y}&=\log_7{\left(2^5\right)}-\log_7{\left(y^2\right)}\\
&=\log_7{32}-\log_7{\left(y^2\right)}
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
\log_7{\left(32\right)}-\log_7{\left(y^2\right)}&=\log_7{\left(\frac{32}{y^2}\right)}\\
\end{align*}
