Question 103956: Please solve 1/2log(4x+5)=logx
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve 1/2log(4x+5)=logx
log(4x+5)^(1/2) = logx
Since the logs are equal the anit-logs are equal:
(4x+5)^(1/2) = x
Square both sides to get:
4x+5 = x^2
x^2-4x-5 = 0
(x-5)(x+1) = 0
x = 5 or x = -1
Checking these answersin the original equation:
If x=5, (1/2)log(20+5) = log 5
log(25)^(1/2) = log 5
log(5) = log 5
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If x=-1, (1/2)log(1) = log(-1)
But log(-1) does not exist so
x=-1 is extraneous.
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Final answer: x=5
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Cheers,
Stan H.
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