Question

The solution of the equation ${\log }_7{\log }_5(\sqrt{x+5}+\sqrt{x})=0$ is

Answer 1

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

$\Rightarrow {\log }_5(\sqrt{x+5}+\sqrt{x})=7^0=1$
$\Rightarrow \sqrt{x+5}+\sqrt{x}=5^1=5$
$\Rightarrow \sqrt{x+5}=5-\sqrt{x}$

Squaring both side,

$\Rightarrow x+5=25+x-10\sqrt{x}$

$\Rightarrow \sqrt{x}=2\Rightarrow x=4$

Ans: 4