#### Answer

$\log_a [(z+7)^5(2z+9)]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Laws of Logarithms to write the given expression, $
5\log_a (z+7)+\log_a (2z+9)
,$ as a single logarithm.
$\bf{\text{Solution Details:}}$
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log_a (z+7)^5+\log_a (2z+9)
.\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_a [(z+7)^5(2z+9)]
.\end{array}