We can simplify the left-hand side of the equation as follows:
(√7)^6x = (7^(1/2))^(6x) = 7^(3x)
We can simplify the right-hand side of the equation as follows:
49^(x-6) = (7^2)^(x-6) = 7^(2(x-6)) = 7^(2x-12)
So the equation becomes:
7^(3x) = 7^(2x-12)
We can solve for x by equating the exponents:
3x = 2x - 12
x = -12
Therefore, the solution to the equation is x = -12