Question

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

Answer 1

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

${\log }_5\left(\sqrt{x+5}+\sqrt{x}\right)=7^2=1$

$\sqrt{x+5}+\sqrt{x}=5$

$x+5+x+2\sqrt{x}\sqrt{x+5}=25$

$2x+5+2\sqrt{x}\sqrt{x+5}=25$

$2\sqrt{x}\sqrt{x+5}=20-2x$

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

$x\left(x+5\right)=100+x^2-20x$

$x^2+5x=x^2-20x+100$

$25x=100$

$x=4$