Answer
$\log_2x+\log_2y-\log_2t-\log_2q-\log_2r$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of radicals and the properties of logarithms to rewrite the given expression, $
\log_2\dfrac{xy}{tqr}
.$
$\bf{\text{Solution Details:}}$
Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\log_2(xy)-\log_2(tqr)
.\end{array}
Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\log_2(xy)-(\log_2t+\log_2q+\log_2r)
\\\\=
\log_2(xy)-\log_2t-\log_2q-\log_2r
\\\\=
\log_2x+\log_2y-\log_2t-\log_2q-\log_2r
.\end{array}
