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!

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- Oct 29th 2012, 04:28 AMJonTKKSolving a non-linear equation
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! - Oct 29th 2012, 05:14 AMJJacquelinRe: Solving a non-linear equation
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.