Answer
$y=-\displaystyle \frac{1}{2}$
Work Step by Step
Definition of the logarithmic function:
For $x>0$ and $b>0, b\neq 1,$
$y=\log_{b}x$ is equivalent to $b^{y}=x$.
So, $\log_{100}0.1=y$ means that $100^{y}=0.1$
(solve for y)
$ 100^{y}=0.1\qquad$ recognize powers of 10
$(10^{2})^{y}=10^{-1}$
$10^{2y}=10^{-1}$
...if the bases are equal, so must be the exponents
2$y=-1$
$y=-\displaystyle \frac{1}{2}$
