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Analytical logarithms

  1. Jan 24, 2013 #1

    joo

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    What is the analytical method for solving log. eqs., like x=2^x/14 ?

    In highschool they only teach us the graphical approach =/

    joo
     
  2. jcsd
  3. Jan 24, 2013 #2

    jedishrfu

    Staff: Mentor

  4. Jan 24, 2013 #3

    joo

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    What I meant was x=(2^x)/14, but I guess that doesn't really change the principle.

    Thanks, I'll take a look at it, although I find myself doubtful.
     
  5. Jan 24, 2013 #4
    There is no analytical solution to your problem. One can express the solutions using the product log function, but that is just another way of writing it, not a true analytic solution.
     
  6. Jan 24, 2013 #5

    I like Serena

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    Homework Helper

    Welcome to PF, joo! :smile:


    In university they still use the graphical approach. ;)

    In addition they use approximation algorithms, like the method of Newton-Raphson (which is based on a Taylor series expansion).

    It's only the really bold ones in math that use the Lambert W function, which is a function that has only been invented to be able to write the solution to your equation.
    As far as I know, no one really uses it.

    The first solution for your equation is ##x=-{W(-\frac 1 {14} \ln(2)) \over \ln(2)} \approx 0.07525##.
     
    Last edited: Jan 24, 2013
  7. Jan 24, 2013 #6

    jedishrfu

    Staff: Mentor

    (HUMOR)

    But Lambert used it and they made a movie on his life among sheep:



    (/HUMOR)
     
    Last edited by a moderator: Sep 25, 2014
  8. Jan 24, 2013 #7

    I like Serena

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    Oh! So the W comes from Walt Disney! :D
     
    Last edited by a moderator: Sep 25, 2014
  9. Jan 24, 2013 #8

    joo

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    Thank you for your replies ! I'll stick to the graphical solving for now then, since I will have no access to any calculators during my tests.
     
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