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Re: Re: Log[4]==2*Log[2]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50696] Re: [mg50635] Re: Log[4]==2*Log[2]
*From*: DrBob <drbob at bigfoot.com>
*Date*: Fri, 17 Sep 2004 01:16:20 -0400 (EDT)
*References*: <chp8q9$jjm$1@smc.vnet.net> <200409150549.BAA11722@smc.vnet.net>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
> In my view two symbolic expressions are not necessarily equal if
> numerically they are equal.
Log[4] and 2Log[2] are numbers. If they are numerically equal, in what sense can they be unequal? It may be impossible to _verify_ exact equality, of course, without manipulating the expressions used to define them.
Perhaps by numerically equal you mean "equal to machine (or other) precision".
Bobby
On Wed, 15 Sep 2004 01:49:34 -0400 (EDT), Peter Valko <p-valko at tamu.edu> wrote:
> Andreas,
>
> In my view two symbolic expressions are not necessarily equal if
> numerically they are equal.
>
> What you wish to know is if the left and right hand sides can be
> brought to a standard form and then if the standard forms are equal.
> To achieve this you may wright:
>
> (Log[4] // Simplify) == (2*Log[2] // Simplify)
>
> that gives a solid True.
>
>
> Regards
> Peter
>
>
>
>
>
> Andreas Stahel <sha at hta-bi.bfh.ch> wrote in message news:<chp8q9$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
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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