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Re: Simplify problems for checking easy equalities...

• To: mathgroup at smc.vnet.net
• Subject: [mg53865] Re: Simplify problems for checking easy equalities...
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Tue, 1 Feb 2005 04:08:15 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

On 1/30/05 at 3:18 AM, cyruserik at tele2.se (Cyrus Erik Eierud) wrote:

>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?

You are not doing something wrong. The reason FullSimplify and Simplify don't work here is that Log[x^n] isn't equal to n Log[x] in general. For example consider n = 2 and x = -2. Log[x^n] would evaluate to Log[4] a real number while n Log[x] evaluates to 2 Log[-2] a complex number.

However you can achieve what you want using PowerExpand, i.e.,

In[1]:= PowerExpand[Log[x^n] - n*Log[x]]
Out[1]= 0
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