Answer
$\log_3{x} + \frac{1}{2}\log_3{y}$
Work Step by Step
RECALL:
(1) $\log_b{(PQ)} = \log_b{P} + \log_b{Q}$
(2) $\sqrt{a} = a^{\frac{1}{2}}$
(3) $\log_b{a^x} = x \cdot \log_b{a}$
Use rule (1) above to obtain:
$=\log_3{x} + \log_3{\sqrt{y}}$
Use rule (2) above to obtain:
$=\log_3{x} + \log_3{y^{\frac{1}{2}}}$
Use rule (3) above to obtain:
$=\log_3{x} + \frac{1}{2}\log_3{y}$