Question

If $4^{2x}=\frac{1}{32}$ then $x$ is

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $\frac{3}{5}$
• D. $-\frac{5}{4}$

Answer 1

The correct option is D $-\frac{5}{4}$

Given,

$4^{2x}=\frac{1}{32}$
$\Rightarrow (2^2{)}^{2x}=\frac{1}{2^5}$
$\Rightarrow (2{)}^{4x}=2^{-5}$

As bases are equal, we can equate the powers,

$\Rightarrow 4x=-5$
$\Rightarrow x=-\frac{5}{4}$
Option D is correct.