Answer
$= \log \frac{\sqrt {15xy^{5}}}{z^{4}} $
Work Step by Step
$\frac{1}{2} \log 5 + \frac{1}{2} \log 3x + \frac{5}{2} \log y - 4 \log z$
$= \log \sqrt 5 + \log \sqrt {3x} +\log \sqrt {y^{5}} - \log z^{4}$
$= \log \sqrt {5(3x)(y^{5})}- \log z^{4}$
$= \log \sqrt {15xy^{5}} - \log z^{4}$
$= \log \frac{\sqrt {15xy^{5}}}{z^{4}} $