Question 532366: I am not sure how to answer this 9^x-3^(x+1)+1=0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am not sure how to answer this
9^x-3^(x+1)+1=0
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(3^x)^2 - 3^x*3 + 1 = 0
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(3^x)^2 - 3(3^x) + 1 = 0
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Let w = 3^x:
w^2 - 3w + 1 = 0
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w = [3 +- sqrt(9-4*1*1)]/2
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w = [3 +- sqrt(5)]/2
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w = (3/2)+(1/2)sqrt(5) or w = (3/2)-(1/2)sqrt(5)
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Solve for "x"
3^x = (3/2)+(1/2)sqrt(5) or 3^x = (3/2)-(1/2)sqrt(5)
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x = ln[(3/2)+sqrt(5)/2}/ln(3) or x = ln[(3/2)-(sqrt(5)/2)/ln(3)
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Cheers,
Stan H.
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