To solve the equation 2^x = 2^(2x-6), we can use the property of exponents that states if two exponential expressions with the same base are equal, then their exponents must be equal.

Therefore, we can set the exponents equal to each other:

x = 2x - 6

Next, we can isolate the variable x by subtracting 2x from both sides:

x - 2x = -6

Simplifying, we get:

- x = -6

Finally, we can solve for x by multiplying both sides by -1:

x = 6

So the solution to the equation 2^x = 2^(2x-6) is x = 6.