The Maxima command 'mnewton' has a bug.
The problem may be solved by updating to the most recent build of Maxima.
{{{
sage: mnewton([x1+3*log(x1)-x2^2, 2*x1^2-x1*x2-5*x1+1], [x1, x2], [5, 5])
[[x1=3.756834008012769,x2=2.779849592817897]]

sage: mnewton([2*a^a-5],[a],[1])
[[a=1.70927556786144]]

sage: mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
Traceback (most recent call last):
...
TypeError: error evaluating "mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);":
Error executing code in Maxima
CODE:
 mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
Maxima ERROR:

Unable to convert 18.0*log(3)+0.5 to a complex double float
#0: 
solve_by_lu(eqs=[h[1]*(18.0*log(3)+0.5)-0.5*h[2]+12.0,4.0*h[2]*log(2)+h[1]+2.0],vars=[h[1],h[2]],field=complexfield)
#1: 
mnewton(funclist=[-v/u+2*3^u-5,2^v+u-4],varlist=[u,v],guesslist=[2,2])(mnewton.mac
line 106)

sage: build_info()$
Maximaversion:5.13.0Maximabuilddate:18:511/18/2008hosttype:x86_64-unknown-linux-gnulisp-implementation-type:CLISP
lisp-implementation-version:2.41(2006-10-13)(built3409699542)(memory3409699897)
}}}

The build_info() command indicates Sage is using Maxima 5.13.
I submitted the problem to Maxima Support and they said it works for
Maxima 5.14.
http://sourceforge.net/tracker/index.php?func=detail&atid=104933&aid=1909488&group_id=4933
{{{
Date: 2008-03-07 15:21
Sender: willisbl
Logged In: YES
user_id=895922
Originator: NO

It works for me; maybe you have an old version.

(%i2) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
(%o2) [[u=1.066618389595407,v=1.552564766841786]]

(%i8) build_info();
Maxima version: 5.14.0
Maxima build date: 21:46 12/27/2007
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8
}}}

Peace

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