Question

5 raise to the power 2x-1 minus 25 raise to the power x-1 is equal to 2500 kindly give stepwise solution

Answer 1

Solution:-
5²ˣ⁻¹ - 25ˣ⁻¹ = 2500
⇒ 5²ˣ⁻¹ - (5²)ˣ⁻¹ = 2500
⇒ 5²ˣ⁻¹ - 5²ˣ⁻² = 2500
⇒ 5²ˣ⁻¹(1 - 1/5) = 2500
⇒ 5²ˣ⁻¹(4/5) = 2500
⇒5²ˣ⁻¹ = (2500*5)/4
⇒ 5²ˣ⁻¹ = 3125
⇒ 5²ˣ⁻¹ = 5⁵
⇒ 2x-1 = 5
⇒ 2x = 5 + 1
⇒ 2x = 6
x = 3
Answer