Answer
$ \displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$
Work Step by Step
.... first, write the square root as a power with exponent 1/2
$...=\displaystyle \log(\frac{x^{2}}{yz^{3}})^{1/2}\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$
$=\displaystyle \frac{1}{2}\log\frac{x^{2}}{yz^{3}}\quad$... Apply the property $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$
$=\displaystyle \frac{1}{2}[\log x^{2}-\log(yz^{3})]\quad$... Apply the property $\log_{a}(MN)=\log_{a}M+\log_{a}N$
$=\displaystyle \frac{1}{2}[\log x^{2}-(\log y+\log z^{3})]$
$=\displaystyle \frac{1}{2}[\log x^{2}-\log y-\log z^{3}]\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$
$=\displaystyle \frac{1}{2}[2\log x-\log y-3\log z]$
$=\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$
