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anonymous
 5 years ago
Use a graphing utility to solve the equation.
ln x=(x^3)3
anonymous
 5 years ago
Use a graphing utility to solve the equation. ln x=(x^3)3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Mathematica 8 was used for this response. "ln" is spelled "Log" below. Refer to the attachment, a plot of x^33Log[x] from x=0 to x=2. To the casual observer the roots are approximately 0.05 and 1.5 . More exact values for the two root are shown below: FindRoot[x^3  3  Log[x], {x, .01}] = .0497932... FindRoot[x^3  3  Log[x], {x, 1.4}] = 1.50499... The symbolic solutions are: \[(1)^{2/3} \left(\frac{1}{3} \text{ProductLog}\left[\frac{3}{e^9}\right]\right)^{1/3} \] \[(1)^{2/3} \left(\frac{1}{3} \text{ProductLog}\left[1,\frac{3}{e^9}\right]\right)^{1/3} \] From the net: ProductLog, or W cannot be expressed in terms of more common elementary functions.
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