Answer
$2\log_a{u}+3\log_a{v}$
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 (3) above to obtain:
$\log_a {(u^2\cdot v^3)}=\log_a{u^2}+\log_a{v^3}$.
Use Rule (2) above to obtain:
$\log_a{u^2}+\log_a{v^3}\\
=2\log_a{u}+3\log_a{v}$
