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Where to start?

  1. May 18, 2008 #1
    Where does one begin to solve the equation 3log(x)=6-2x?
  2. jcsd
  3. May 18, 2008 #2
    The solution to that equation is not expressible in terms of elementary functions.
  4. May 18, 2008 #3


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    Looks like material for Lambert's W (or Newton's method).
  5. May 18, 2008 #4


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    you could use a numerical approach like newton's method to find a solution. if I am not mistaken you can say that x>0 since ln(x) is undefined otherwise and then rewrite your equation as [itex]x^{3}e^{2x}-e^{6}=0[/itex]
  6. Mar 15, 2010 #5
    an approximate solution is possible through pt of intersection of the 2 graphs...but i dont think theres any way to find an exact solution save hit n trial
  7. Mar 15, 2010 #6
    MATLAB's solver gave:

    [tex]\frac{\mathrm{e}^{2}}{\mathrm{e}^{\omega\!\left(\ln\!\left(\frac{2}{3}\right) + 2\right)}}[/tex]

    Where [tex]\omega[/tex] is given by: http://en.wikipedia.org/wiki/Wright_Omega_function.

    Good call by whoever said it needed the Lambert W-function ^_^

    But for practical purposes, just use bisection+newton.
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