Answer
Infinite discontinuity
Work Step by Step
We are given the function:
$f(x)=\ln |x-4|$
Compute the left hand and right hand limits:
$\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\infty$
$\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$
Therefore we got:
$\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$
As the function is not defined in $x=4$ and both its one-sided limits are infinite, the function has an infinite discontinuity.
