Solve the following equations for $x$:$ 2^{3 x-7}=256 $

Given:

\( 2^{3 x-7}=256 \)

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,

$2^{3 x-7}=256$

$2^{3x-7}=(2)^{8}$

Comparing the powers on both sides, we get,

$3x-7=8$

$3x=8+7$

$3x=15$

$x=\frac{15}{3}$

$x=5$

Therefore, the value of $x$ is $5$. 

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Updated on: 10-Oct-2022

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