Maxima Help : Lambert W-Function



Help:?How do I solve these equations in Maxima ?1. x^x=27 (the root is x=3)2. x^(1/x)=(cube root of 3) (the roots are x=3 and?x=-(3W(-(log(3))/3))/(log(3)))3. x^(2*x)=729(the roots are x=3 and x = (i(pi-3i log(3)))/(W(i pi+3log(3))))
but I cannot solve these equations in Maxima!(but I can use Find Root):(%i1) to_poly_solve([x^(2*x)=729], [x]);
Loading maxima-grobner $Revision: 1.6 $ $Date: 2009-06-02 07:49:49 $
Unable to solve
Unable to solve
Unable to solve
(%o1) %solve([x^(2*x)=729],[x])
How can I solve them not by find root?