Question

I need help
How do you find x:
2^(2x) + 2^(x+2) - 12 = 0

Answer 1

`x=1`

Explanation:

`2^(2x)-2^2 2^x-12=0 \\ \\ (2^x)^2-4(2^x)-12=0`

Factoring the quadratic in
`2^x`,

`(2^x+6)(2^x-2)=0 \\ \\ 2^x=-6,2 \\ \\ 2^x=2 \implies x=1 \\ \\ 2^x=-6 \implies x \\otin \mathbb{R} \\ \\ \therefore x=\log_(2) (6)`