Question

If ${\log }_6{\log }_2[\sqrt{4x+2}+2\sqrt{x}]=0$ , then x is .........

Answer 1

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

$4x+2=\left(2\right(1-\sqrt{x}){)}^2=4(1+x-2\sqrt{x})$

$2x+1=2(1+x-2\sqrt{x})$

$let\sqrt{x}=z$

$2z^2+1=2+2z^2-4z$

$1=4z=>z=-\frac{1}{4}$

$\sqrt{x}=-\frac{1}{4}$

$x=\frac{1}{16}$