If $5^{2 x - 1} - (25)^{x - 1} = 2500$ , then the value of $x$ is ____.

2

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5

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3

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1

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Solution

The correct option is B $3$
L.H.S $: 5^{2 x - 1} - 25^{x - 1}$ can be written as
$\Rightarrow 5^{2 x - 1} - 5^{2 x - 2} = 5^{2 x - 1} (1 - \frac{1}{5}) = 5^{2 x - 1} \times \frac{4}{5} = 5^{2 x - 2} \times 4 \dots e q n (1)$

R.H.S $: 2500 = 25^{2} \times 4 = 5^{4} \times 4 \dots e q n (2)$
We have, L.H.S =R.H.S
From equation 1 and 2
$5^{2 x - 2} \times 4 = 5^{4} \times 4 \Rightarrow 2 x - 2 = 4 \Rightarrow 2 x = 6 \Rightarrow x = 3$

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Similar questions

If 5^2x-1 - (25)^x-1 = 2500, then the value of x =?

5^{2 x - 1} - 25^{x - 1} = 2500.

25^{x - 1} = 5^{2 x - 1} - 100

x

25^{(x - 1)} = 5^{(2 x - 1)} - 100

Question:- If 25^x-1 = 5^2x-1 - 100, then the value of x is_____________.

A) 3

B) 2

C) 4

D) 1

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