Answer
Domain: $(-\infty,0)\cup (0,\infty)$
Work Step by Step
We need to find the domain of:
$k(x)=\ln|x|$
We can't take the log of a negative number (or 0), so:
$|x|\gt 0$
$x\gt 0$ or $-x\gt 0$
$x\gt 0$ or $x\lt 0$
In other words, $x$ can be any real number except 0 ($x\neq 0$). Therefore, the domain is: $(-\infty,0)\cup (0,\infty)$.
