FullSimplify[Solve[x^2 + Log[10, 2*x] == 3, x]] Gives x->Sqrt[5/2] in Mathematica Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm ----- Original Message ----- From: "Michael Kleber" <kleber@brandeis.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, April 04, 2003 4:59 PM Subject: Re: [math-fun] transcendental puzzles
Mathematica vs Dan Asimov:
PUZZLE: Given that x^2 + log_10 (2x) = 3, solve for x > 0 in closed form
In[1]:= Solve[ x^2 + Log[10,2x] == 3, x ]
InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses.
Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found.
ProductLog[500000 (Log[2] + Log[5])] Out[1]= {{x -> Sqrt[------------------------------------]}} 2 (Log[2] + Log[5])
Hmm, let's see if it can do any better than that...
In[2]:= Simplify[%]
5 Log[10] Out[2]= {{x -> Sqrt[---------]}} Log[100]
Aah, much better. I have no idea why it fails to recognize Log[10]/Log[100]. I'm not a Mma expert; there's probably some argument you can pass to Simplify to remind it to think about some extra transformation rules...
--Michael Kleber kleber@brandeis.edu
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