Answer
$x=3$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{9}x=\frac{1}{2}$ is equivalent to $9^{\frac{1}{2}}=x$.
Therefore, $x=3$, because $9^{\frac{1}{2}}=\sqrt 9=3$.