Question

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

Answer 1

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