Question

if 25^x-1 = 5^2x-1 - 100 find the value of x

Answer 1

Assuming the question as: 25x – 1 = 52x – 1 – 100
⇒ (52)x – 1 = 52x – 1 – 100
⇒ 52x – 2 = 52x – 1 – 100
⇒100 = 52x – 1 – 52x – 2
⇒ 52x – 1 – (52x – 1)/5 =100 → (1)
Let 52x – 1 = a
Equation (1) becomes,
a – a/5 =100
⇒ 4a/5 =100
⇒ a = (100 × 5)/4 = 125
Therefore, 52x – 1 = 125
⇒ 52x – 1 = 53
⇒ 2x – 1 = 3
⇒ 2x = 4
∴ x = 2