Answer
$x=81$
Work Step by Step
Converting to exponential form, the solution to the given logarithmic equation, $
\log_x{9}=\dfrac{1}{2}
,$ is:
\begin{array}{l}\require{cancel}
x^{1/2}=9
\\\\
\sqrt{x}=9
\\\\
\left( \sqrt{x} \right)^2=(9)^2
\\\\
x=81
.\end{array}