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 > >