Using Lambertw to solve $x\ln(x) = a$

Asked Feb 14 '14 at 17:28

Active Feb 14 '14 at 17:33

Viewed 483 times

I am trying to solve the equation

$$ x \ln (x) = a, $$

where $x$ is a variable and $a$ is a given constant, using Matlab and the lambertw function.

Not really sure exactly what to type into Matlab to solve this equation!

Thanks in advance for any help!

edited Feb 14 '14 at 17:33

Antonio Vargas

asked Feb 14 '14 at 17:28

Kylar

No need for matlab, just write$x \ln x = e^{\ln x}\ln x$, so that you're trying to solve $e^{\ln x}\ln x = a$. Then $\ln x = W(a)$ so $x = e^{W(a)}$. – Antonio Vargas Feb 14 '14 at 17:31
Unfortunately we are supposed to use Matlab for this homework... I completely understand that maths, but what do we type into Matlab for this? would it be lambertw(ln(x)) or...? – Kylar Feb 14 '14 at 17:36
Do you mean just syms a x then solve(x*log(x) == a)? To write this I just looked at this help page, which I found with google. – Antonio Vargas Feb 14 '14 at 17:39
Ahh, yes of course. That's perfect, thank you so much!! – Kylar Feb 14 '14 at 17:43
1

My googling skills are world-renowned. – Antonio Vargas Feb 14 '14 at 17:46
Yeah, I thought it was something to do with using the lambertw function, not using the solve function! :) – Kylar Feb 14 '14 at 17:51
http://www.mathworks.fr/fr/help/symbolic/lambertw.html – Claude Leibovici Feb 15 '14 at 08:48

0 Answers0