To solve this equation, we can first simplify the left side of the equation:

(2x-1)^10 * (1/4)^5
= (2x-1)^10 * 1/1024
= (2x-1)^10 / 1024

Now, we can simplify the right side of the equation:

(X-1/2)^9
= (X-1/2)^9

Since the right side is already simplified, we can set the two sides equal to each other:

(2x-1)^10 / 1024 = (X-1/2)^9

Now, we can solve for x by taking the 9th root of both sides and then simplifying:

(2x-1)^10 = 1024 * (X-1/2)^9
2x-1 = (1024 * (X-1/2)^9)^(1/10)
2x-1 = (X-1/2) * 2
2x-1 = 2X - 1
2x = 2X
x = X

Therefore, the solution to the equation is x = X.