With manual assistance, Maxima can find some, but not all, complex solutions to these equations; example:
(%i12) %solve(log(x^(2*x)=729),x);
(%o12) %union([x=log(729)/(2*lambert_w(log(729)/2))])
(%i13) float(%);
(%o13) %union([x=3.0])
Recently I've been working on code for the generalized Lambert function. It recognizes
simplifications such
(%i21) generalized_lambert_w(-1 ,-log(5)/5);
(%o21) -log(5)
but it will not simplify %o12 to 3. This could be a bug or an oversight. Additionally, the code in to_poly_solve
that solves in terms of the Lambert function needs work. I'm unsatisfied with that code.
Thanks for the interest.
--Barton (author of to_poly_solver)
-----maxima-bounces at math.utexas.edu wrote: -----
To: <maxima at math.utexas.edu>
From: -Henry Hom
Sent by: maxima-bounces at math.utexas.edu
Date: 09/17/2011 04:19PM
Subject: 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? ? ?
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