Question

The value of $x$ satisfying the equation ${\sqrt{3}}^{(-4+2{\log }_{\sqrt{5}}x)}=\frac{1}{9}$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. none of these

Answer 1

The correct option is D none of these

We have, ${\sqrt{3}}^{(-4+2{\log }_{\sqrt{5}}x)}=\frac{1}{9}$
$\Rightarrow {\sqrt{3}}^{(-4+2{\log }_{\sqrt{5}}x)}=9^{-1}=3^{-2}={\left(\sqrt{3}\right)}^{-4}$
Equating the powers of $\sqrt{3}$
$-4+2{\log }_{\sqrt{5}}x=-4$
$\Rightarrow 2{\log }_{\sqrt{5}}x=0$
$\Rightarrow {\log }_{\sqrt{5}}x=0$
Taking exponential of the above equation, we get
$\therefore x={\left(\sqrt{5}\right)}^0=1$