To solve the equation 2^(2x) = 8^9, we can rewrite 8 as 2^3 since 8 is equal to 2 raised to the power of 3.

So the equation becomes: 2^(2x) = (2^3)^9

Using the property of exponents, we can simplify further: 2^(2x) = 2^(3*9)

Since the bases are the same, we can equate the exponents: 2x = 3*9

Simplifying the right side: 2x = 27

To solve for x, divide both sides by 2: x = 27/2

Therefore, x = 13.5.