SOLUTION: x^log(x)= 10000/x What is the product of the solutions? I have simplified it to (log (x))^2 + log (x) = 4, but can't solve that equation.

Question 341176: x^log(x)= 10000/x
What is the product of the solutions?
I have simplified it to (log (x))^2 + log (x) = 4, but can't solve that equation.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^log(x)= 10000/x
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Multiply both sides by x to get:
x*x^[log(x)] = 10000
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Simplify:
x^(1+log(x)] = 10000
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I graphed the left side as Y1 and the right side as Y2.
I found the intersection at x = 36.4379
========================
Cheers,
Stan H.
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