Solve 3^(x^2-77)=9^(2x)

3^(x^2-77)=9^(2x) Solve for x. I got -7,11 i want to make sure its right and please explain how you got your answer. Thanks!

3^(x^2-77)=9^(2x)

the above eqn can be rewritten as

3^(x^2-77)=3^2*(2x) as 9 = 3^2

so now,
3^(x^2-77)=3^(4x)

Lets equate the powers now as the bases are equal

x^2-77 = 4x
or x^2 - 4x -77 = 0

or, x^2 -11x + 7x -77 = 0

or x (x - 11) + 7 (x - 11) = 0

or (x - 11) (x +7 ) = 0

or x = 11 and -7

Your answers
x=-7 or x=11 are right.