Find the values of $x$ in each of the following:$ 5^{2 x+3}=1 $

Given:

\( 5^{2 x+3}=1 \)

To do: 

We have to find the value of $x$.

Solution:

We know that,

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

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

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

$a^{0}=1$

Therefore,

$5^{2 x+3}=1$

$\Rightarrow 5^{2x+3}=5^{0}$

Comparing both sides, we get,

$2x+3=0$

$\Rightarrow 2x=-3$

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

The value of $x$ is $\frac{-3}{2}$.      

Tutorialspoint

Updated on: 10-Oct-2022

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