Question

If ${\log }_7({\log }_5\sqrt{x+5}+{\log }_5\sqrt{x+5})$= 0, then find the value of $x$.

Answer 1

${\log }_7({\log }_5\sqrt{x+5}+{\log }_5\sqrt{x+5})=0$

$\Rightarrow {\log }_7\left(2{\log }_5\sqrt{x+5}\right)=0$

$\Rightarrow 2\log \sqrt{x+5}=7^0=1$

$\Rightarrow {\log }_5(x+5)=1$

$\Rightarrow x+5=5^1=5$

$\Rightarrow x=5-5=0$

$\therefore x=0$.