Answer
$3\log x+\dfrac{1}{2}\log y-\log z$
Work Step by Step
Using the properties of logarithms, the given expession, $
\log\dfrac{x^3\sqrt{y}}{z}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\log\left(x^3\sqrt{y}\right)-\log z
&(\text{use }\log_b \dfrac{x}{y}=\log_b x-\log_b y)
\\\\&=
\log x^3+\log\sqrt{y}-\log z
&(\text{use }\log_b (xy)=\log_b x+\log_b y)
\\&=
\log x^3+\log y^{1/2}-\log z
\\&=
3\log x+\dfrac{1}{2}\log y-\log z
&(\text{use }\log_b x^y=y\log_b x)
.\end{align*}
Hence, the expression $
\log\dfrac{x^3\sqrt{y}}{z}
$ is equivalent to $
3\log x+\dfrac{1}{2}\log y-\log z
$.
