Ah! Now, here's an answer I like!
Now, all you need to do is have an algorithm to try to transform
equations into the P(F(X))=C format!
> > Out of 4 problems I submitted to the community (problems I took out of a
> > Maple class I'm teaching), it turns out that Maxima can solve quite well
> > 2 of them (through tricks I people gave me). Both Mathematica and Maple
> > can solve all 4 problems. I only kept one problem (the exp one), because
> > I'm convinced Maxima should be able to solve it.
>
> You'll find the explanation in the documentation for the solve
> command, DESCRIBE(SOLVE);
>
> It says that SOLVE deals with equations of the form P(F(X))=C where P
> is a polynomial (quadratic, cubic, etc) and F is an invertible
> function. The equations exp(a*x)=C*exp(b*x) and a^x = b^x do not fall
> into that class, hence it does not attempt to solve them.
>
>
--
Daniel Lemire, Ph.D.
http://www.ondelette.com