Question

If 5²ˣ⁻¹ = 25ˣ⁻¹ + 100, find the value of 3¹⁺ˣ.

Answer 1

x = 2

3¹⁺ˣ = 27

Explanation:

5²ˣ⁻¹ = 25ˣ⁻¹ + 100

5²ˣ⁻¹ - 25ˣ⁻¹ = 100

5²ˣ⁻¹ - (5²)ˣ⁻¹ = 4 * 5²

5²ˣ⁻¹ - 5²ˣ⁻² = 4 * 5²

5^(2x - 3) - 5^(2x - 4) = 4

5^(2x - 4) * (5 - 1) = 4

5^(2x - 4) *4 = 4

5^(2x - 4) = 1

2x - 4 = 0

2x = 4

x = 2

3¹⁺ˣ = 3^(1 + 2) = 3^3 = 27