To solve this equation, we need to simplify both sides and then isolate the variable.

On the left side:
x^(log4(x) - 2) = x^(log4(x)) / x^2 = x^(log4(x)) / 4

On the right side:
2^(3*(log4(x-1))) = 2^(log4((x-1)^3)) = (x-1)^3

Now we have:
x^(log4(x)) / 4 = (x-1)^3

To further simplify, we can rewrite x^(log4(x)) as x^(log(x) / log(4)) = x^(log(x) / 2) since log(4) = 2.

So, we have:
x^(log(x) / 2) / 4 = (x-1)^3

To isolate x, we need to bring everything to one side:
x^(log(x) / 2) / 4 - (x-1)^3 = 0

This equation does not have a simple algebraic solution, and therefore needs to be solved numerically using methods such as graphing or numerical approximations.