Answer
$x=\frac{1}{49}$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $log_{x}\frac{1}{7}=\frac{1}{2}$ is equivalent to $x^{\frac{1}{2}}=\sqrt x=\frac{1}{7}$.
$x=\frac{1}{49}$, because $(\frac{1}{7})^{2}=\frac{1}{49}$