Question

Find $x$ if $3^{-x}=\frac{1}{3^2}.$

• A. $-3$
• B. $3$
• C. $-2$
• D. $2$

Answer 1

The correct option is D $2$

Given that $3^{-x}=\frac{1}{3^2}.$
$⟹3^{-x}\times 3^2=1$
$⟹3^{-x+2}=1(\because a^m\times a^n=a^{m+n})$
$⟹3^{-x+2}=3^0(\because a^0=1)$
$⟹2-x=0(\because a^m=a^n⟹m=n,\text{where}a\ne 0,-1,1)$
$⟹x=2$