Solving a non-linear equation

Oct 2012
1
0
Singapore
Hi all,

given a non-linear equation f(x)=X+[(lnX)/3]-2

How do I find X when f(x)=0? I have problems getting rid of the ln(x)


Many thanks!
 
Aug 2011
252
76
In practice, one use numerical computation to obtain an approximate value of the root (with the wanted accuracy). x=1.803435512117243497937275089140621551695008634858815...
The closed form, thanks to the Lambert W function, is :
x = (1/3)*W(X) where X=3*exp(6)
There is no simpler formula with elementary functions.