Answer
$\log_3{u}+2\log_3{v}-\log_3{w}$
Work Step by Step
Recall:
(1) $\log_a{(mn)}=\log_a{m} + \log_a{n}$
(2) $\log_a{\left(\frac{m}{n}\right)}=\log_a{m} - \log_a{n}$
(3) $\log_a{a^m}=m\log_a{m}$
Use rule (2) above to obtain:
\begin{align*}
\log_3{\left(\frac{uv^2}{w}\right)}-\log_3{w}&=\log_3{\left(uv^2\right)}-\log_3{w}
\end{align*}
Use rule (1) above to obtain:
\begin{align*}
\log_3{\left(uv^2\right)}-\log_3{w}&=\log_3{u}+\log_3{v^2}-\log_3{w}
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
\log_3{u}+\log_3{v^2}-\log_3{w}&=\log_3{u}+2\log_3{v}-\log_3{w}
\end{align*}
