Answer
$\log_3{u}+2\log_3{v}-\log_3{w}$
Work Step by Step
Recall:
(1) $\sqrt[m]{a}=a^{\frac{1}{m}}$
(2) $\log_a {x^n}=n\cdot \log_a {x}$.
(3) $\log_a{xy}=\log_a{x} +\log_a{y}$
(4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$
($\log_a{M}=\log_a{N} \longrightarrow M=N$.)
Using Rule(4): $\log_3{\frac{uv^2}{w}}=\log_3{uv^2}-\log_3{w}.$
Using Rule(3): $\log_3{uv^2}-\log_3{w}=\log_3{u}+\log_3{v^2}-\log_3{w}$
Using Rule(2): $\log_3{u}+\log_3{v^2}-\log_3{w}=\log_3{u}+2\log_3{v}-\log_3{w}$
