Answer
$\log\sqrt{xy}$
Work Step by Step
$\displaystyle \frac{1}{2}(\log x+\log y) \quad $...apply the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
$=\displaystyle \frac{1}{2}\cdot \log (xy)\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\log(xy)^{1/2}=\log\sqrt{xy}$
