Answer
$2\log_a{u} + 3 \log_a{v}$
Work Step by Step
Recall:
$\log_a{(MN)} = \log_a{M}+\log_a{N}$
Using the rule above gives:
$\log_a (u^2 v^3) = \log_a{\left(u^2\right)} + \log_a{\left(v^3\right)}$
With $\log_a M^r = r \log_a M$, then the equation above simplifies to:
$\log_a (u^2 v^3) = \boxed{2\log_a u + 3 \log_a v}$
