Answer
(a) $x=-\frac{100\log 2}{\log 5}$
(b) $x\approx -43.067656$
Work Step by Step
(a) We need to solve:
$5^{-x/100}=2$
We take the log of both sides and use log rules to simplify:
$\log 5^{-x/100}=\log 2$
$-\frac{x}{100}\log 5=\log 2$
$-\frac{x}{100}=\frac{\log 2}{\log 5}$
$x=-\frac{100\log 2}{\log 5}$
(b) We solve using a calculator:
$x\approx -43.067656$
