Answer
{10}
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{x}\frac{1}{10}=-1$ means the same as $x^{-1}=\frac{1}{10}$.
We know that $x=10$, because $10^{-1}=\frac{1}{10}$.