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.

```

• Prev by Date: Re: Common factors in a list
• Next by Date: Re: Common factors in a list
• Previous by thread: Re: exact integer from Log[ ]