Answer
$\dfrac{1}{3}\log_a x+2\log_a z\Rightarrow
\log_a (x^{1/3}z^2)
$.
Work Step by Step
Using the properties of logarithms, the given expression, $\dfrac{1}{3}\log_a x+2\log_a z,$ is equivalent to
\begin{align*}
&
\log_a x^{1/3}+\log_a z^2
&(\log x^y=y\log x)
\\&=
\log_a (x^{1/3}z^2)
&(\log (xy)=\log x+\log y)
.\end{align*}Hence, $
\dfrac{1}{3}\log_a x+2\log_a z$ is equivalent to $
\log_a (x^{1/3}z^2)
$.
