Answer
$\log_b x+2\log_b y-\log_b w-3\log_b z$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_b \dfrac{xy^2}{wz^3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_b (xy^2)-\log_b (wz^3)
\\\\=
\log_b x+\log_b y^2-\left( \log_b w+\log_b z^3 \right)
\\\\=
\log_b x+\log_b y^2-\log_b w-\log_b z^3
\\\\=
\log_b x+2\log_b y-\log_b w-3\log_b z
.\end{array}
