Answer
$x=-\dfrac{100\log2}{\log5}\approx-43.067656$
Work Step by Step
$5^{-x/100}=2$
Apply $\log$ to both side of the equation:
$\log5^{-x/100}=\log2$
The exponent $-x/100$ can be taken down to multiply in front of its respective $\log$:
$-\dfrac{x}{100}\log5=\log2$
Solve for $x$:
$-x=\dfrac{100\log2}{\log5}$
$x=-\dfrac{100\log2}{\log5}\approx-43.067656$
