(1/4)^x * (64/25)^x = (5/4)^2

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To solve this equation, we can first rewrite each term with the same base to make it easier to compare:

(1/4)^x = (1/4)^x * 1

(64/25)^x = ((64/25)^(1/2))^2x = (8/5)^2x

Now, we can rewrite the original equation using these expressions:

(1/4)^x * (64/25)^x = (5/4)^2

(1/4)^x * (8/5)^2x = (5/4)^2

Simplify the equation further:

(1/4)^x * (64/25)^x = (25/16)

(1/4)^x * (8/5)^2x = (25/16)

Now we can equate the powers of the terms with the same base:

1/4 = 25/16

Since the bases are not the same, the equation has no solution, and it is not possible to solve for x in this case.