# What does log(0) equal?

$\log \left(0\right)$ is undefined.
Basically you are trying to find a value of $x$ such that ${e}^{x} = 0$.
As a real valued function ${e}^{x}$ maps $\left(- \infty , \infty\right)$ to $\left(0 , \infty\right)$, so its inverse, $\log$, maps $\left(0 , \infty\right)$ to $\left(- \infty , \infty\right)$.
$\log \left(x\right)$ is undefined for $x \le 0$