Question

Find the value of x​

Answer 1

5²ˣ⁻¹-25ˣ⁻¹ = 2500

or, 5²ˣ⁻¹-5²⁽ˣ⁻¹⁾ = 5²×5²×2²

or, 5⁽²ˣ⁻¹⁾-5⁽²ˣ⁻²⁾ = 5⁴×2²

or, 5⁽²ˣ⁻¹⁾(1-5⁻¹) = 5⁴×2²

or, 5⁽²ˣ⁻¹⁾(1-¹/₅) = 5⁴×2²

or, 5⁽²ˣ⁻¹⁾×⁴/₅ = 5⁴×2²

or, 5⁽²ˣ⁻¹⁾ = 5⁴×2²×⁵/₄

or, 5⁽²ˣ⁻¹⁾ = 5⁴×4×⁵/₄

or, 5⁽²ˣ⁻¹⁾ = 5⁵

Since, the bases in both sides are equal,

2x-1 = 5

or, 2x = (5+1)

or, 2x = 6

or, x = ⁶/₂

or, x = 3

Hence, the value of x is 3.

Hope this helps you to get to your answer.