Question

Solve ${\log }_{0.2}|x-3|\ge 0$
What is the maximum possible value that $x$ can take?

Answer 1

${\log }_{0.2}|x-3|\ge 0\Rightarrow 0<|x-3|\le {\left(0.2\right)}^0$
$\Rightarrow$ $0<|x-3|\le 1\Rightarrow -1<x-3\le 1$ and $x-3\ne 0$
$\Rightarrow$ $2<x\le 4$ and $x\ne 3\Rightarrow xϵ(2,4]-\left\{3\right\}$
Ans: 4