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