How do you solve 4^(2x) + 4^x + 12 = 042x+4x+12=0?

1 Answer
Aug 5, 2015

There is no real solution.

Explanation:

4^(2x) + 4^x + 12 = 042x+4x+12=0

(4^x)^2 + 4^x + 12 = 0(4x)2+4x+12=0

You can do a replacement: u = 4^xu=4x

u^2 + u +12=0u2+u+12=0

u = (-1+-sqrt(1^2-4(1)(12)))/2u=1±124(1)(12)2

= (-1+-sqrt(-47))/2=1±472

uu is imaginary so we would need 4^x4x is imaginary and whie that is certainly possible for imaginary xx, it is not normally handled in a precalculus study of mathematics.

There is no real solution.