Question

Solve exactly in terms of ln or log. be sure to check solutions: 2^2x + 2^x - 12 = 0

Answer 1

solve as a quadratic in \[2^x\] say put
\[z=2^x\] and then solve
\[z^2+2z-12=0\]
\[z=-1+\sqrt{13}\]
\[2^x=-1+\sqrt{13}\]
\[x=\log_2(-1+\sqrt{13})\]