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

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Solution

Consider, 5^2x – 1 – (5^2)^x – 1 = 2500
⇒ 5^2x – 1 – 5^2x – 2 = 2500
⇒ 5^2x – 1 – (5^2x – 1)/5 = 2500 → (1)
Let 5^2x – 1 = a
Equation (1) becomes,
a – a/5 = 2500
⇒ 4a/5 = 2500
⇒ a = (2500 × 5)/4 = 3125
Therefore, 5^2x – 1 = 3125
⇒ 5^2x – 1 = 5^5
⇒ 2x – 1 = 5
⇒ 2x = 6
∴ x = 3

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