SOLUTION: i need help with this problem: 2^2x+ 2^x - 12=0 This is what i tried, but i think it's wrong: I tried to factor out: (2^x+6)(1^x-2), and now i am totally lost! pls help!

Question 377689:
i need help with this problem: 2^2x+ 2^x - 12=0
This is what i tried, but i think it's wrong:
I tried to factor out: (2^x+6)(1^x-2), and now i am totally lost! pls help! Thx! Pls note: the "2x" and the "x" are exponents of the numbers 2. difficult to show that on this screen.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need help with this problem: 2^2x+ 2^x - 12=0
----
It's a quadratic written in 2^x.
---
Let w = 2^x
----
w^2 + w -12 = 0
Factor:
(w+4)(w-3) = 0
w = -4 or w = 3
----
Solve for "x":
2^x = -4
Impossible
----
2^x = 3
x = ln3/ln2
x = 1.4651..
================
Cheers,
Stan H.
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