Answer
$x=\frac{1}{49}$
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, $log_{x}\frac{1}{7}=\frac{1}{2}$ is equivalent to $x^{\frac{1}{2}}=\frac{1}{7}$.
Therefore, $x=\frac{1}{49}$, because $(\frac{1}{49})^{\frac{1}{2}}=\sqrt \frac{1}{49}=\frac{1}{7}$.