Find the value of x in 125^x-2 + 125^x-3 = 125^x-4.with explanation

125^x-2 = 125^2 * 125^x-4

125^x-3 = 125 * 125^x-4
so, what we have is

125^x-4 (125^2 - 125) = 125^x-4
125^2 - 125 = 1
No solution

Evidently I misunderstood the notation. If you meant

125^x - 2 + 125^x - 3 = 125^x - 4
125^x = 1
x = 0