Given : #160; 5^3x+1=25^x+2 ⇒5^3x+1=(5^2)^x+2 ⇒5^3x+1=5^2x+4 Equating the powers with the same base, we get ⇒ 3x+1=2x+4 ⇒ 3x 2x=4 1=3 ...

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Comparision of Quantities Using Exponents

Solve: 53x+1...

Question

Solve: $5^{3 x + 1} = 25^{x + 2}$

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Solution

Given : $5^{3 x + 1} = 25^{x + 2}$

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

$\Rightarrow 5^{3 x + 1} = 5^{2 x + 4}$

Equating the powers with the same base, we get

$\Rightarrow 3 x + 1 = 2 x + 4$

$\Rightarrow 3 x - 2 x = 4 - 1 = 3$

$∴ x = 3$

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