Answer
There is a discontinuity when $a=1$
The limit $\lim\limits_{x \to 1}k(x)$ does not exist.
Work Step by Step
We are given $k(x)=\ln|\frac{x}{x-1}|$
There is a discontinuity when $a=1$
The limit $\lim\limits_{x \to 1}k(x)$ does not exist.