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MathGroup Archive 2004

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Re: Re: Log[4]==2*Log[2]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50660] Re: [mg50635] Re: Log[4]==2*Log[2]
  • From: Andrzej Kozlowski <andrzej at akikoz.net>
  • Date: Wed, 15 Sep 2004 07:54:34 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This approach is not always a good idea. Besides being inefficient 
(Simplify used twice) you can get:


Simplify[Im[Sqrt[-1 + eta^2]], -1 < eta < 1] ==
   Simplify[Sqrt[eta^2 - 1], -1 < eta < 1]

Im[Sqrt[eta^2 - 1]] == Sqrt[eta^2 - 1]

when in fact:


Simplify[Im[Sqrt[-1 + eta^2] - Sqrt[eta^2 - 1]],
    -1 < eta < 1] == 0

True

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/




On 15 Sep 2004, at 14:49, Peter Valko wrote:

> *This message was transferred with a trial version of CommuniGate(tm) 
> Pro*
> Andreas,
>
> In my view two symbolic expressions are not necessarily equal if
> numerically they are equal.
>
> What you wish to know is if the left and right hand sides can be
> brought to a standard form and then if the standard forms are equal.
> To achieve this you may wright:
>
> (Log[4] // Simplify) == (2*Log[2] // Simplify)
>
> that gives a solid True.
>
>
> Regards
> Peter
>
>
>
>
>
> Andreas Stahel <sha at hta-bi.bfh.ch> wrote in message 
> news:<chp8q9$jjm$1 at smc.vnet.net>...
>> To whom it may concern
>>
>> the following answer of Mathematica 5.0 puzzeled me
>>
>> Log[4]==2*Log[2]
>> leads to
>>
>> N::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached 
>> while \
>> evaluating -2\Log[2]+Log[4]
>>
>> with the inputs given as answer. But the input
>>
>> Log[4.0]==2*Log[2]
>>
>> leads to a sound "True"
>>
>> Simplify[Log[4]-2*Log[2]]
>> leads to the correct 0, but
>> Simplify[Log[4]-2*Log[2]==0]
>> yields no result
>>
>> There must be some systematic behind thid surprising behaviour.
>> Could somebody give me a hint please
>>
>> With best regards
>>
>> Andreas
>
>


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