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Re: exact integer from Log[ ]

• To: mathgroup at smc.vnet.net
• Subject: [mg58337] Re: exact integer from Log[ ]
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 28 Jun 2005 21:56:37 -0400 (EDT)
• Organization: The Open University, Milton Keynes, England
• References: <d9r4o7$54g$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Trevor Baca wrote:
> The question is how to get the exact integer 13 when we let
> 
>   f = 880*2^(1/12)
> 
> and let
> 
>   expr = Log[2^(1/12), f/440]
> 
> with no numerics (only exact integers) in both expressions.
> 
> It seems that expr should already equal the integer 13 exactly, yet
> evaluating expr gives
> 
>   (12*Log[2*2^(1/12)])/Log[2]
> 
> or
> 
>   Log[8192]/Log[2]
> 
> with Simplify[expr], which, while clearly 13 to the eye, still isn't
> exactgly 13 on the page.
> 
> So how do you get 13 back out of expr, preferably without recourse to
> numerics?
> 
> 
> Trevor.
> 
Hi Trevor,

If I remember correctly, *Simplify* does very few attempt to manipulate 
exponents. So, try one of the following commands

In[24]:=
FullSimplify[expr]

Out[24]=
13

In[25]:=
PowerExpand[expr]

Out[25]=
13

In[26]:=
FunctionExpand[expr]

Out[26]=
13

Best regards,
/J.M.