Answer
$\left\{\dfrac{1}{2}\right\}$
Work Step by Step
Since $\log_b y=x$ implies $b^x=y$, the given equation, $
x=\log_93
$, implies
\begin{align*}\require{cancel}
9^x&=3
.\end{align*}
Expressing both sides of the equation above in the same base results to
\begin{align*}\require{cancel}
\left(3^2\right)^x&=3
\\\\
3^{2x}&=3^1
.\end{align*}
Since $b^x=b^y$ implies $x=y$, the equation above implies
\begin{align*}\require{cancel}
2x&=1
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
\dfrac{\cancel2x}{\cancel2}&=\dfrac{1}{2}
\\\\
x&=\dfrac{1}{2}
.\end{align*}
Hence, the solution set of the equation $
x=\log_93
$ is $
\left\{\dfrac{1}{2}\right\}
$.
