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)
In practice, one use numerical computation to obtain an approximate value of the root (with the wanted accuracy). x=1.8034355121172434979372750891406215516950086348 58815...
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.