SOLUTION: 4^x-20.2^x+64=0 , find X

Question 222906: 4^x-20.2^x+64=0 , find X
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4^x-20.2^x+64=0 , find X
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It looks like a quadratic:
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(2^x)^2 - 20(2^x) + 64 = 0
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Let w = 2^x
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Rewrite:
w^2 - 20w + 64 = 0
w^2 - 4w-16w + 64 = 0
w(w-4)-16(w-4) = 0
(w-4)(w-16) = 0
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w = 4 or w = 16
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Substitute to solve for "x":
2^x = 4 or 2^x = 16
x = 2 or x = 4
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Cheers,
Stan H.
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