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To solve this equation, we need to first simplify the left side of the equation using the properties of logarithms.

log9 3^(2x-9) = 2

Using the power rule of logarithms, we can rewrite the left side of the equation as:

(2x - 9) * log9 3 = 2

Now, we can isolate the variable by dividing both sides by log9 3:

2x - 9 = 2 / log9 3

Now, we can solve for x by adding 9 to both sides and then dividing by 2:

2x = 2 / log9 3 + 9

x = (2 / log9 3 + 9) / 2

x = (1 / log9 3 + 9/2)

Therefore, the solution to the equation log9 3^(2x-9) = 2 is x = (1 / log9 3 + 9/2).