Question

If the domain of $g\left(x\right)=\ln (2x-8)$ is $(a,\infty )$.Find $a$

Answer 1

We have, $g\left(x\right)=\ln (2x-8)$

Clearly, $g\left(x\right)$ assumes real values if

$2x-8>0$

$\Rightarrow 2x>8$

$\Rightarrow x>4$

So, Domain of $g\left(x\right)=(4,\infty )$

Hence $a=4$