[scantor145]

How do you solve the following:

y = x + ln x

[ebaines]

What do you mean by "solve?" Are you asking if there's a way to solve for x given a value for y? Or do you mean you want to find the root(s) of this equation (i.e. for y = 0)?

[Capuchin]

Indeed, I would say it's already solved for y ;)

[scantor145]

What do you mean by "solve?" Are you asking if there's a way to solve for x given a value for y? Or do you mean you want to find the root(s) of this equation (i.e., for y = 0)?

I want to solve for x, as in x + ln x = 10.
I believe I've found out that one needs to use Newton's method to get a very close approximation. I think that the Solver add-in in Excel will do the trick.

I've also heard that a function, Lambert W, will solve it exactly.

[ebaines]

With the exception of obvious solutions such as x + ln(x) = 1, I don't know of a closed form solution for this, so using an approximation technique like Newton's method is a good approach.