## anonymous one year ago Hi everyone : hope ur well so I have this log plus absolute question so. For ln (x-2) = ln (2-x) I know there is no solution however for ln |x-2| = ln |2-x| There is , someone can kindly how is that possible and also help me solve this thank u

1. perl

I don't think there is a solution in either case.

2. anonymous

$\ln|x-2|=\ln\left(|-1||2-x|\right)=\ln|2-x|$

3. anonymous

You can think of the absolute value terms $$|2-x|$$ and $$|x-2|$$ in terms of distance. The distance between $$x$$ and $$2$$ is always the same. $$|a-b|$$ can be read as "the distance from $$a$$ to $$b$$", and $$|b-a|$$ as "the distance from $$b$$ to $$a$$". You can expect the distance to be the same regardless of the starting point.