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Find x

  1. Jun 12, 2010 #1
    1. The problem statement, all variables and given/known data
    4^x = x^4. My instructor wants me to find the answer that is -0.77, not 2 or 4. And showing work as well.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 13, 2010 #2
    Did you try graphing the equations and finding where they intercept?
     
    Last edited: Jun 13, 2010
  4. Jun 13, 2010 #3

    HallsofIvy

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    There is no "formula" or elementary function that will solve that. I would try to get it into a form in which I could use Lambert's W function- it is defined as the inverse of [itex]xe^x[/itex].
     
  5. Jun 13, 2010 #4
    If you detail you calculations so far perhaps then can advice with this :smile:
     
  6. Jun 13, 2010 #5
    I tried using log but I keep getting stuck at xlog2=2logx
     
  7. Jun 13, 2010 #6
    Make a quick sketch of the two functions. Just use the range [itex]-2 \leq x \leq 2[/itex] and plot the two lines together. From the graph you should be able to see the intersect and hence the answer you require. :smile:
     
  8. Jun 13, 2010 #7

    HallsofIvy

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    Why are you ignoring my post? That equation cannot be solved using elementary functions. Do a numerical solution, or graph as Axiom17 and Immutef have suggested, or use Lambert's W function.
     
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