Solve the following equations for $x$:$ 2^{5 x+3}=8^{x+3} $

Given:

\( 2^{5 x+3}=8^{x+3} \)

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,

$2^{5x+3}=8^{x+3}$

$2^{5x+3}=(2^{3})^{x+3}$

$2^{5x+3}=2^{3 x+9}$

Comparing the powers on both sides, we get,

$5x+3=3 x+9$

$5x-3x=9-3$

$2x=6$

$x=\frac{6}{2}$

$x=3$

Therefore, the value of $x$ is $3$.  

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Updated on: 10-Oct-2022

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