Question 464917: Solve for x: 2^(2x) + 2^(x+2) - 12 = 0, I do believe logarithms are to be used to simplify.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve for x: 2^(2x) + 2^(x+2) - 12 = 0,
I do believe logarithms are to be used to simplify
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(2^x)^2 + (2^x)*4 - 12 = 0
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(2^x)^2 + 4*(2^x) - 12 = 0
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Note: Quadratic form with variable 2^x
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Let 2^x = w
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w^2 + 4w - 12 = 0
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Factor:
(w+6)(w-2) = 0
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w = -6 or w = 2
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Solve for "x":
2^x = -6 or 2^x = 2
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Note: No power of 2 can be negative so 2^x = -6 is meaningless.
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2^x = 2
x = 1 (this is the only solution for the problem)
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Cheers,
Stan H.
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