Answer
$\left\{\dfrac{1}{9}\right\}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_3(9x+8)=2
$, implies
\begin{align*}\require{cancel}
9x+8&=3^2
\\
9x+8&=9
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
9x+8-8&=9-8
\\
9x&=1
\\\\
\dfrac{\cancel9x}{\cancel9}&=\dfrac{1}{9}
\\\\
x&=\dfrac{1}{9}
.\end{align*}
Hence, the solution set of the equation $
\log_3(9x+8)=2
$ is $
\left\{\dfrac{1}{9}\right\}
$.
