Find the value of $x$ for which $5^{2x} \div 5^{-3}= 5^{5}$.

Given:

$5^{2x} \div5^{-3}= 5^{5}$.

To do:  

We have to find the value of \( x \).

Solution:

We know that,

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

$5^{2 x}\div 5^{-3}=5^{5}$

$5^{2 x} \times 5^{3}=5^{5}$

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

Comparing both sides, we get,

$2x+3=5$

$2x=5-3$

$2x=2$

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

$x=1$

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Updated on: 10-Oct-2022

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