Solve the following equations for $x$:$ 7^{2 x+3}=1 $

Given:

\( 7^{2 x+3}=1 \)

To do:

We have to find the value of $x$.

Solution:

We know that,

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

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

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

$a^{0}=1$  

$7^{2 x+3}=1$

$7^{2 x+3}=7^{0}$

Comparing the powers on both sides, we get,

$2 x+3=0$

$2 x=-3$

$x=\frac{-3}{2}$

Therefore, the value of $x$ is $\frac{-3}{2}$.

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Updated on: 10-Oct-2022

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