1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook