Question

Solve:${\log }_e{\log }_5[\sqrt{2x-2}+3]=0$

Answer 1

${\log }_e{\log }_5[\sqrt{2x-2}+3]=0$

$\Rightarrow {\log }_5[\sqrt{2x-2}+3]=e^0=1$

$\Rightarrow {\log }_5[\sqrt{2x-2}+3]=1$

$\Rightarrow \sqrt{2x-2}+3=5^1=5$

$\Rightarrow \sqrt{2x-2}=5-3=2$

$\Rightarrow 2x-2=4$

$\Rightarrow 2x=4+2=6$

$\Rightarrow 2x=6$

$\Rightarrow x=\frac{6}{2}=3$

$\therefore x=3$