SOLUTION: solve for x : 1-log5 x =log5 (x-1)

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Question 1086813: solve for x : 1-log5 x =log5 (x-1)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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1-log5 x =log5 (x-1)
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If this is for log of base 5,
1-log%285%2Cx%29=log%285%2C%28x-1%29%29

log%285%2C%28x-1%29%29%2Blog%285%2Cx%29=1

log%285%2C%28%28x-1%29%29%2Ax%29%29=1

5%5E1=x%28x-1%29
5=x%5E2-x
x%5E2-x-5=0
system%28x=%281-sqrt%281%2B4%2A5%29%29%2F2%2Cor%2Cx=%281%2Bsqrt%281%2B4%2A5%29%29%2F2%29

You want the choice that makes the log inputs positive:
cross%28x=%281-sqrt%2821%29%29%2F2%29,or,highlight%28x=%281%2Bsqrt%2821%29%29%2F2%29