Question

Solve exactly in terms of ln or log: 2^2x + 2^x - 12 = 0

Answer 1

let u=2^x
then u^2=2^(2x)

so you have u^2+u-12=0
(u+4)(u-3)=0
u=-4, u=3
but remember u=2^x

2^x=-4, 2^x=3
but you throw out 2^x=-4 because when you take natural log of both sides you get natural log of a negative which does not exist
so just solve 2^x=3 and you are done