Answer
$\log_2 3+\log_2 x+2\log_2y$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_23xy^2
$, is equivalent to
\begin{align*}\require{cancel}
&
\log_2 3+\log_2 x+\log_2y^2
&(\text{use }\log_b (xy)=\log_b x+\log_b y)
\\&=
\log_2 3+\log_2 x+2\log_2y
&(\text{use }\log_b x^y=y\log_b x)
.\end{align*}
Hence, the expression $
\log_23xy^2
$ is equivalent to $
\log_2 3+\log_2 x+2\log_2y
$.
