Answer
$\log_3{\left(\frac{u^2}{v}\right)}$
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) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$
Use Rule (2) to obtain
$2\log_3{u}-\log_3{v}=\log_3{u^2}-\log_3{v}$
Use Rule (4) above to obtain
$\log_3{u^2}-\log_3{v}=\log_3{\left(\frac{u^2}{v}\right)}$
