Hi
In this question How I know 0,000001 = 10^-2
Is there a way ? Is there a way by Calculator ?
Remember that $\displaystyle \log_a{b}=c \Longleftrightarrow\ a^{c} = b$, with $\displaystyle \log_a{b}=c$ well defined.
What it's written in yor exercise is just the aplication of the above.
Thus, you know $\displaystyle \log_b{0,0001}=-2 \Longleftrightarrow\ b^{-2}=0,0001$, but also know $\displaystyle 0,0001=10^{-4}=(10^{2})^{-2}$, because a propertie of powers says $\displaystyle (a^{b})^{c}=a^{bc}$ with $\displaystyle (a^{b})^{c}$ well defined.
Therefore, $\displaystyle b=100$