How is $Y=-2\ln(X-5)$ distributed when $X \sim \mathcal{U}(5,6)$?

Question

How is $Y$ distributed while $X \sim \mathcal{U}(5,6)$ and $Y=-2\ln(X-5)$?

I reached to $\mathbb{P}\left[X>e^{-y/2}+5\right]$ and i'm not sure about that too.

Answer 1

Indeed. $\Bbb P[Y\leqslant y]~{ =\Bbb P[-2\ln(X-5)\leqslant y]\\=\Bbb P[X\geqslant\exp(-y/2)+5]}$

Now use $\Bbb P[X\geqslant x]=(6-x)\mathbf 1_{x\in[5..6]}+\mathbf 1_{x\leq 5}$ where $x=\exp(-y/2)+5$.