Question

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

Answer 1

$x=4$, We have
$lo{g}_{7}lo{g}_5[\sqrt{x+5}+\sqrt{x}]=0$
$\Rightarrow lo{g}_5[\sqrt{x+5}+\sqrt{x}]=7^o=1$
$\Rightarrow \sqrt{x+5}+\sqrt{x}=5$
$\Rightarrow \sqrt{x+5}=5-\sqrt{x}$
$\Rightarrow x+5=25+x-10\sqrt{x}$
$\Rightarrow 2=\sqrt{x}$
$\Rightarrow x=4$.