Question 148322: Find the value of x in logx + 1/logx = 5/2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the value of x in logx + 1/logx = 5/2
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Multiply thru by 2logx to get:
2(logx)^2 + 2 = 5logx
Rearrange:
2(logx)^2 - 5logx + 2 = 0
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This is a quadratic with variable logx:
Let logx = w and substitute:
2w^2 -5w + 2 = 0
Factor using the AC Method:
2w^2-4w-w+2 = 0
2w(w-2)-(w-2) = 0
(w-2)(2w-1) = 0
w = 2 or w = 1/2
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Substiute back to logx:
logx = 2 or logx = 1/2
x = 10^2 or x = 10^(1/2)
x = 100 or x = sqrt(10)
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Cheers,
Stan H.
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