# How do you evaluate g(x)=log_bx for x=b^-3?

$g \left({b}^{-} 3\right) = - 3$
In general, ${\log}_{a} {a}^{n} = n$, because ${\log}_{a} b$ is the power $a$ must be raised to, to get $b$. So, in our case, $- 3$ is the power $b$ needs to be raised, in order to get ${b}^{-} 3$. ${\log}_{b} {b}^{-} 3 = - 3$.