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Re: Simplify problems for checking easy equalities...


On 2/2/05 at 6:25 AM, kjm at KevinMcCann.com (Kevin J. McCann) wrote:

>While your approach works, the identity is true regardless of the
>values of x and n; so, it is curious that Simplify does not get it
>for the more general case.

No, the identity is not true regardless of the values of x and n. For a specific counter example, choose x = -1 and n = 2. The Log[x^n] = Log[1] = 0 and n Log[x] = 2 Log[-1] = 2 Pi I which is clearly not 0.

>David Park wrote:
>>Cyrus,
>>
>>Include the proper assumptions in the Simplify statement.
>>
>>Simplify[Log[x^n] - n*Log[x], n \[Element] Integers && x > 0] 0
>>
>>David Park djmp at earthlink.net http://home.earthlink.net/~djmp/
>>
>>From: Cyrus Erik Eierud [mailto:cyruserik at tele2.se]
To: mathgroup at smc.vnet.net
>>
>>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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