Compare a V graph with a logarithm across a pole

The logarithm requires $(x-1)^2>0$, so $x\ne1$. It has vertical asymptote $x=1$. Sketch $y=|x+2|$ and $y=\ln((x-1)^2)$ on the same axes. The source gives intersections approximately $(-5.85,3.85)$ and $(-0.812,1.19)$. Read where the V graph is on or above the logarithm: in the printed three-significant-figure form, $x\leq-5.85$ or $-0.812\leq x<1$ or $x>1$.

Let $\alpha<\beta<1$ be the two exact intersection inputs satisfying $|x+2|=\ln((x-1)^2)$. Numerically $\alpha\approx-5.847877501$ and $\beta\approx-0.811590083$. The exact set is $(-\infty,\alpha]\cup[\beta,1)\cup(1,\infty)$. The displayed source decimals are rounded graph readings, not exact thresholds.