To solve the equation 7^(2x-6) = 49, we can start by rewriting 49 as 7^2 since 49 is equal to 7 raised to the power of 2.

So, the equation becomes 7^(2x-6) = 7^2.

Since the bases are the same, we can equate the exponents:

2x - 6 = 2.

Now, we can solve for x by isolating the variable:

2x = 2 + 6.

2x = 8.

Dividing both sides by 2:

x = 8/2.

x = 4.

Therefore, the solution to the equation 7^(2x-6) = 49 is x = 4.