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!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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!       Log On


   

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