Find the values of $x$ in each of the following:
$ 2^{5 x} \p 2^{x}=\sqrt[5]{2^{20}} $

Given:

\( 2^{5 x} \div 2^{x}=\sqrt[5]{2^{20}} \)

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,

$2^{5 x} \div 2^{x}=\sqrt[5]{2^{20}}$

$\Rightarrow \frac{2^{5 x}}{2^{x}}=(2^{20})^{\frac{1}{5}}$

$\Rightarrow 2^{5 x-x}=2^{\frac{20}{5}}$

$\Rightarrow 2^{4 x}=2^{4}$

Comparing both sides, we get,

$4 x=4$

$\Rightarrow x=1$

The value of $x$ is $1$. 

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Updated on: 10-Oct-2022

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