Solve 2 (25^x) = 3 - 5^x

Hello:

25 = 5²

25^x = (5²) ^x = (5^x) ²

let : 5^x = t ... t > 0

the equation : 2 (25^x) = 3 - 5^x equiv:

2t² = 3 - t and : 5^x = t ... t > 0

2t² + t - 3 = 0

the discriminant : Δ = b² - 4ac = (1) ² - 4 (2) (-3) = 25 = 5²

t1 = (-1-5) / 4 (refused : t > 0)

t2 = (-1+5) / 4 = 1

but: 5^x = t

5^x = 1

the solution is : x=0