Chapter 12 - Section 12.5 - Logarithmic Functions - Exercise Set - Page 876: 91

We can't have negative numbers as the logarithmic base since, if we raised a negative number to a fractional power, we could end up with a negative number under a radical. We aren't dealing with imaginary numbers, so this would not provide a real number answer.

$log_b n =e$ $b=-2$, $n$ is unknown, $e=1/4$ $b^e=n$ $(-2)^{1/4}=\sqrt[4] {-2}$ $\sqrt[4] {-2}=i\sqrt[4] 2$