Is $\ln (x/y) = \ln |x| - \ln |y|$?

The expression $\ln(x/y)$ only makes sense when $x/y>0$. In this specific case we have, $x>0$ and $y>0$, or, $x<0$ and $y<0$. When ($x>0$ and $y>0$) or ($x<0$ and $y<0$), we can write,

$$\frac xy=\frac{|x|}{|y|}$$ and then,

$$\ln (x/y)=\ln |x|-\ln |y|.$$