Thread: type of exponential equation

To solve could you use Lambert W function?

Thanks

It can be solved via derivatives and intersections of curves. But how would you solve it in a purely algebraic manner using the W Lambert function?

Originally Posted by tukeywilliams

It can be solved via derivatives and intersections of curves. But how would you solve it in a purely algebraic manner using the W Lambert function?

In principle yes it can, the equation can be transformormrd to:



So formaly we have:



Now the problem is that there a multiple (real) branches of the Lambert W in
the region around , and you are going to have to
evaluate two of them to get all the solution to this. My LambertW calculator
gives .

However just plot the functions and you will see that there is another
solution near Numerical methods will find both solutions
once you know where they are.

RonL

Here is a graph if you'd like to see...

Originally Posted by CaptainBlack

...there is another solution near ...

RonL

I really couldn't see that one when looking at the graph...

Originally Posted by janvdl

I really couldn't see that one when looking at the graph...

A binary search gives me about x = 22.440006

-Dan