Question

Find $x$, if $4^{2x}=\frac{1}{32}$.

• A. $\frac{5}{4}$
• B. $\frac{-5}{4}$
• C. $\frac{-4}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is B

$\frac{-5}{4}$

Given, $4^{2x}=\frac{1}{32}$

$\Rightarrow$ $4^{2x}=\frac{1}{2^5}$

$\Rightarrow$ $(2^2{)}^{2x}=2^{-5}$
$[\because a^{-m}=\frac{1}{a^m}]$

$\Rightarrow$ $2^{4x}=2^{-5}$
$[\because (a^m{)}^n=\left(a{)}^{m\times n}\right]$

Since the bases are equal, the exponents should also be equal.

$\Rightarrow$ $4x=-5$

$\Rightarrow$ $x=\frac{-5}{4}$