Answer
$\log_3 m+\log_3 n-\log_3 5-\log_3 r$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of logarithms to rewrite the given expression, $
\log_3 \dfrac{mn}{5r}
.$
$\bf{\text{Solution Details:}}$
Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log_3 (mn)-\log_3 (5r)
.\end{array}
Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log_3 m+\log_3 n-(\log_3 5+\log_3 r)
\\\\=
\log_3 m+\log_3 n-\log_3 5-\log_3 r
.\end{array}
