To solve this exponential equation, we need to rewrite it in terms of a common base.

First, let's rewrite the bases so that they are the same:

(0,4)^x-1 = (6,25)^(6x-5)
(2^2)^x-1 = (2*3)^6x-5

Now simplify the bases:

2^(2x-2) = 6^(6x-5)

Next, let's rewrite 6 as 2*3:

2^(2x-2) = (23)^(6x-5)
2^(2x-2) = 2^(1(6x-5))

Since the bases are the same, we can say:

2x-2 = 1*(6x-5)

Now let's solve for x:

2x - 2 = 6x - 5
2 = 4x - 5
7 = 4x
x = 7/4

Therefore, the solution to the equation is x = 7/4.