Question 305490: ln(x+3)/ln(x-3)=2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ln(x+3)/ln(x-3)=2
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ln(x+3) = 2ln(x-3)
ln(x+3) = ln(x-3)^2
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x+3 = (x-3)^2
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x^2 - 6x + 9 = x+3
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x^2 -7x +6 = 0
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(x-6)(x-1) = 0
x = 6 or x = 1
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Checking in ln(x+3)/ln(x-3)=2
Check x = 6: ln(9)/ln(3) = 2
ln(9) = 2ln(3)
ln(9) = ln9
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Check x = 1: ln(4)/ln(-2) = 2
No because ln(-2) does not exist.
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Only solution: x = 6
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Cheers,
Stan H.
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