#### Answer

$\log_a [(z+1)^2(3z+2)]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Laws of Logarithms to write the given expression, $
2\log_a (z+1)+\log_a (3z+2)
,$ 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+1)^2+\log_a (3z+2)
.\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+1)^2(3z+2)]
.\end{array}