Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: an expression with logs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75385] Re: an expression with logs
  • From: Norbert Marxer <marxer at mec.li>
  • Date: Fri, 27 Apr 2007 05:29:13 -0400 (EDT)
  • References: <f0n78d$qdg$1@smc.vnet.net>

On 25 Apr., 11:33, dimitris <dimmec... at yahoo.com> wrote:
> Hello.
>
> In[27]:=
> oo = 5*Log[4/3] - 3*Log[3/2] - Log[2];
>
> I want oo to take the form 4*(3*Log[2] - 2*Log[3])
>
> I can think one workaround like
>
> In[43]:=
> PowerExpand[oo]
> Collect[%, {Log[2], Log[3]}]
> % /. Log[4] -> 2*Log[2]
> Factor[%]
>
> Out[43]=
> -Log[2] - 3*(-Log[2] + Log[3]) + 5*(-Log[3] + Log[4])
>
> Out[44]=
> 2*Log[2] - 8*Log[3] + 5*Log[4]
>
> Out[45]=
> 12*Log[2] - 8*Log[3]
>
> Out[46]=
> 4*(3*Log[2] - 2*Log[3])
>
> But I am sure there is something smarter and more compact.
>
> Any ideas?
>
> Dimitris

Hello

This version should work on arbitrary rational and integer numbers.
(Note that I didn't test it thoroughly though).

f1 := #1 /. Log[Rational[x_, y_]] :>
     Log[x] - Log[y] &
f2 := #1 /. Log[x_Integer] :>
     Plus @@ f3 /@ FactorInteger[x] &
f3[{x_, y_}] := y*Log[x];
f := Expand[f2[f1[#1]]] &

Then

f[Log[24]]
f[5*Log[4/3] - 3*Log[3/2] - Log[2]]
f[Log[(3*4^3)/5^2]]

will give you

3*Log[2] + Log[3]
12*Log[2] - 8*Log[3]
6*Log[2] + Log[3] - 2*Log[5]

Best Regards
Norbert Marxer




  • Prev by Date: Re: How to make a loop for this problem!
  • Next by Date: Re: How to make a loop for this problem!
  • Previous by thread: an expression with logs
  • Next by thread: how to create a subclass