Question

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

Answer 1

There is no real solution.

Explanation:

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

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

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

`u^2 + u +12=0`

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

`= (-1+-sqrt(-47))/2`

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

There is no real solution.