Question

If $3^x=\frac{1}{81}$, then the value of $x$ is

• A. 4
• B. -2
• C. -4
• D. 2

Answer 1

The correct option is C

-4

$\text{Given,}{3}^x=\frac{1}{81}=\frac{1}{3^4}=3^{-4}[\because \frac{1}{a^m}=(a{)}^{-m}]$
i.e., $3^x=3^{-4}$
Since bases are equal, powers must also be equal.
$\Rightarrow x=-4$