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Analytical logarithms 
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#1
Jan2413, 11:57 AM

P: 6

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
Jan2413, 12:25 PM

P: 3,097

I suppose you could replace the 2^(x/14) with its taylor series expansion and then cutoff some terms to get an approximation:
http://en.wikipedia.org/wiki/Taylor_series 


#3
Jan2413, 12:37 PM

P: 6

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
Jan2413, 01:28 PM

P: 825

Analytical logarithms
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
Jan2413, 01:31 PM

HW Helper
P: 6,189

Welcome to PF, joo!
In university they still use the graphical approach. ;) In addition they use approximation algorithms, like the method of NewtonRaphson (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##. 


#6
Jan2413, 01:38 PM

P: 3,097

But Lambert used it and they made a movie on his life among sheep: http://www.youtube.com/watch?v=LRtKAQJUc3g (/HUMOR) 


#8
Jan2413, 02:50 PM

P: 6

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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