Find all solutions to 4^x - 2^x = 56 + 11*2^x + 2^(x - 1).
Only 4
\(4^x - 2^x = 56 + 11\cdot 2^x + 2^{x - 1}\)
If we let \(t = 2^x\) we have
\(t^2 - t = 56 + 11t + \dfrac12 t\\ 2t^2 - 25t - 112 = 0\\ (t - 16)(2t + 7) = 0\)
It is not possible that 2^x = -7/2, therefore 2^x = 16, which corresponds to x = 4.
