Question

If $9^n=\frac{9}{3^n}$ the value of $n$ is:

• A. $\frac{4}{3}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $2$

Answer 1

Answer: (C)

$\frac{2}{3}$

$9^n=\frac{9}{3^n}$

$\Rightarrow (3^2{)}^n=\frac{3^2}{3^n}$

$\Rightarrow 3^{2n}=3^{2-n}$

$\because$ Base is same on both sides of the equation

$\therefore 2n=2-n$

$\Rightarrow 2n+n=2$

$\Rightarrow n=\frac{2}{3}$