Solve the following equations for $x$:$ 4^{2 x}=\frac{1}{32} $

Given:

\( 4^{2 x}=\frac{1}{32} \)

To do:

We have to find the value of $x$.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  

Therefore,

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

$(2^2)^{2x}=2^{-5}$

$2^{4x}=2^{-5}$

Comparing the powers on both sides, we get,

$4x=-5$

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

Therefore, the value of $x$ is $\frac{-5}{4}$.  

Tutorialspoint

Updated on: 10-Oct-2022

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