Question

.................... solve 1 ​

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