Answer
$x=7$
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, $log_{x}49=2$ is equivalent to $x^{2}=49$. Since $x\gt0$, we know that $x=7$, as $7^{2}=49$.