Question

The maximum possible value of $x$ for the inequality ${\log }_3(x-2)\le 2$ is

Answer 1

${\log }_3(x-2)\le 2$
For $\log$ to be defined, $x-2>0$
$\Rightarrow x>2...\left(1\right)$

Now, $x-2\le 3^2$
$\Rightarrow x\le 11...\left(2\right)$
From $\left(1\right)$ and $\left(2\right),$ we get
$2<x\le 11$