SOLUTION: x^x=100, find x.
I have tried using newton raphson method but i got stock on the way when lambert w. Function come to play. Please i need the solution as well as lambert w. Func
Question 1046218: x^x=100, find x.
I have tried using newton raphson method but i got stock on the way when lambert w. Function come to play. Please i need the solution as well as lambert w. Function interretation. Thanks in advance Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! x^x = 100
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W is the product log or lambert function
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x = e^(W(2(ln(2)+ln(5))))
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note that x^x = e^(xlnx) for x>0
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To get you started
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If x = W (z), then xe^× = z
x^x = 100
xlnx = ln100
(lnx)e^(lnx) = ln100, I used x = e^(lnx)
lnx = W(ln100) by definition of W
x = e^W(ln100)
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we can graph two equations y=100 and y=x^x
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intersection point is approx 3.6
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