3^(2x)+28=11(3^x)

Question

I can't figure out how to start solving it. Haven't used this site before, please help?

I have to find the exact solution in simplified form.

Answer 1

Let u = 3^x > 0. Collect all terms in one side,

u^2 - 11u + 28 = (u-4)(u-7) = 0

u = 3^x =  4, 7

x = ln4/ln3, or ln7/ln3 <==Answer