Solving xlnx = c + dx w/ Lambert's W Func.

[kayhm]

Homework Statement

Can I solve for xlnx = c + dx using Lambert's W function?

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

Homework Statement

Can I solve for xlnx = c + dx using Lambert's W function?

Homework Equations

The Attempt at a Solution

Yes you can.

I've given the first three steps... after that, it shouldn't be too hard to finish:

$$x log(x) = c + d x$$

$$log(x) = \frac{c}{x} + d$$

$$log\left(\frac{cx}{c}\right) = \frac{c}{x} + d$$

$$log(c) + log\left(\frac{x}{c}\right) = \frac{c}{x} + d$$

Can you continue?

 

[kayhm]

Thanks so much.

 

[Char. Limit]

Thanks so much.

It's no problem at all.