# Analytical logarithms

1. Jan 24, 2013

### joo

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. Jan 24, 2013

### Staff: Mentor

3. Jan 24, 2013

### joo

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. Jan 24, 2013

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. Jan 24, 2013

### I like Serena

Welcome to PF, joo!

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
6. Jan 24, 2013

### 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
7. Jan 24, 2013

### I like Serena

Oh! So the W comes from Walt Disney! :D

Last edited by a moderator: Sep 25, 2014
8. Jan 24, 2013

### joo

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.