Question

The value of ‘x’, when $3^x=\frac{\sqrt{3}}{9}$ is:

• A. $\frac{-3}{2}$
• B. $\frac{2}{3}$
• C. $-2$
• D. $3$

Answer 1

The correct option is A

$\frac{-3}{2}$

$3^x=\frac{\sqrt{3}}{9}$
${9.3}^x=\sqrt{3}$
$3^2.3^x=(3{)}^{\frac{1}{2}}$

$\because a^m\times a^n=a^{(m+n)}$

$\Rightarrow 3^{2+x}=(3{)}^{\frac{1}{2}}$
Since bases are equal powers should also be equal
$\Rightarrow x+2=\frac{1}{2}$
$x=\frac{1}{2}-2=\frac{-3}{2}$