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 - 52 = 4x - 57 = 4xx = 7/4
Therefore, the solution to the equation is x = 7/4.
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.