Question

Find the value of ‘x’, when $3^x=\frac{\sqrt{3}}{9}$.

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

Answer 1

The correct option is A $\frac{-3}{2}$

$3^x=\frac{\sqrt{3}}{9}$
$9\times 3^x=\sqrt{3}$
$3^2\times 3^x=(3{)}^{\frac{1}{2}}$
$3^{2+x}=3^{\frac{1}{2}}[a^m\times a^n=a^{m+n}]$

By equating the powers:
$x+2=\frac{1}{2}$
$x=\frac{1}{2}-2=\frac{-3}{2}$