Answer
$x=10$
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, $log_{x}100=2$ is equivalent to $x^{2}=100$.
Therefore, $x=10$, because $10^{2}=100$.