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MathGroup Archive 2005

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Re: Simplify problems for checking easy equalities...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53882] Re: Simplify problems for checking easy equalities...
  • From: "adamizer" <adam.smith at hillsdale.edu>
  • Date: Tue, 1 Feb 2005 04:08:44 -0500 (EST)
  • References: <cti5nd$8n2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

This is a common difficulty when getting used to Mathematica.
Mathematica assumes that all variables are complex and Log[x^n] does
not reduce to n Log[x] when n is complex.  It also is not true for x<0

What you want is to tell Mathematica the specific conditions - They are
called "Assumptions" in Mathematica.  The following illustrates this.
Look in the Help under Simplify.  It has a nice set of examples of
using Simplify with Assumptions.

Simplify[Log[x^n], {Element[n, Reals], x > 0 }]

With exponents and logs the function PowerExpand[] is very useful and
does these assumptions automatically.

PowerExpand[Log[x^n]]

Adam





Cyrus Erik Eierud wrote:
> Please Help!
>
> Thanks for all great answers I've already found here!
> My problem is that I can not simplify what to me seems as a very
> simple equality task. This is what I want Mathematica to return zero
> for:
>
> in[1]:= FullSimplify[Log[x^n] - n*Log[x]]
>
> out[1]= -n Log[x] + Log[x^n])
>
> I have used Simplify to check equalities, but the one above (and many
> other equations similar to the one above) just don't simplify. Am I
> doing anything wrong or does anyone know of a better way to check
> equalities?
> 
> Appreciate any help,
> Cyrus Eierud, Student
> cyruserik at tele2.se



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