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Homework Help: Equation: solve for t.

  1. Dec 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve for t: [tex]t^{t^2}=k[/tex]

    2. Relevant equations

    [tex] Y=Xe^X \iff X=W(Y) [/tex]

    3. The attempt at a solution

    [tex] t^{t^2} = k [/tex]

    [tex] t = k^{1\over t^2} [/tex]

    [tex] t = e^{{1\over t^2} ln (k)} [/tex]

    [tex] {1\over t} ln(k) = {1\over t^2} ln(k) e^{{1\over t^2} ln(k)} [/tex]

    [tex] t = \sqrt{ln(k)\over {W({{1\over t} ln(k)})}} [/tex]
     
  2. jcsd
  3. Dec 19, 2009 #2
    This isn't right by the way. I'm wondering how to get to the right answers.
     
  4. Dec 19, 2009 #3
    [tex] t^{t^2} = k [/tex]

    [tex] t^{2{t^2}} = k^2 [/tex]

    [tex] t^2= k^{2\over t^2} [/tex]

    [tex] t^2 = e^{{2\over t^2}ln(k)} [/tex]

    [tex] 2ln(k) = {2ln(k)\over t^2}e^{{2\over t^2}ln(k)} [/tex]

    [tex] W(2ln(k)) = {2ln(k)\over t^2} \Rightarrow t = \pm \sqrt{2ln(k) \over W(2ln(k))} [/tex]
     
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