Analytical logarithms

  • Thread starter joo
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  • #1
joo
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Main Question or Discussion Point

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

In highschool they only teach us the graphical approach =/

joo
 

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  • #2
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  • #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.
 
  • #4
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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.
 
  • #5
I like Serena
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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##.
 
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  • #6
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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.
(HUMOR)

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


(/HUMOR)
 
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  • #7
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(HUMOR)

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


(/HUMOR)
Oh! So the W comes from Walt Disney! :D
 
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  • #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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