SOLUTION: Solve : 3(2^(2x)) - 2^(x+2) +1=0 I am having real trouble with this one , I hope someone can help me:)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve : 3(2^(2x)) - 2^(x+2) +1=0 I am having real trouble with this one , I hope someone can help me:)      Log On


   

Question 132874: Solve : 3(2^(2x)) - 2^(x+2) +1=0
I am having real trouble with this one , I hope someone can help me:)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve : 3(2^(2x)) - 2^(x+2) +1=0
3(2^(2x) -[2^x*2^2] + 1 = 0
3(2^2x) -4(2^x] + 1 = 0
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Let 2^x = w
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Rewrite the equation in "w":
3w^2 -4w + 1 = 0
Factor:
(3w-1)(w-1) = 0
w = 1/3 or w = 1
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Rewrite in terms of "x":
2^x = (1/3) or 2^x = 1
x = [log(1/3)]/[log2] or x = [log1]/[log2]
x = -1.58496... or x = 0
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Cheers,
Stan H.