Question

The value of x satisfying the equation ${\log }_{17}{\log }_5(5\sqrt{x}-\sqrt{25x-4})=0$ is ..............
find $50\ast \sqrt{x}$ ?

Answer 1

${\log }_{17}{\log }_5(5\sqrt{x}-\sqrt{25x-4})=0$
$\Rightarrow {\log }_5(5\sqrt{x}-\sqrt{25x-4})={17}^0=1$
$\Rightarrow 5\sqrt{x}-\sqrt{25x-4}=5^1=5\Rightarrow 5(\sqrt{x}-1)=\sqrt{25x-4}$
Squaring both sides, $25(x+1-2\sqrt{x})=25x-4\Rightarrow 50\sqrt{x}=29\Rightarrow x={\left(\frac{29}{50}\right)}^2$