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Re: Working with Log

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112117] Re: Working with Log
  • From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
  • Date: Tue, 31 Aug 2010 04:17:00 -0400 (EDT)

Hi, Themis,
one idea may be as follows. Introduce two functions for expansion and to collect logarithms:

expandLog[expr_] := Module[{rule1, rule2, a, b, x},
   rule1 = Log[a_*b_] -> Log[a] + Log[b];
   rule2 = Log[a_^x_] -> x*Log[a];
   (expr /. rule1) /. rule2
   ];
collectLog[expr_] := Module[{rule1, rule2, a, b, x},
   rule1 = Log[a_] + Log[b_] -> Log[a*b];
   rule2 = x_*Log[a_] -> Log[a^x];
   (expr /. rule1) /. rule2 /. rule1 /. rule2
   ];

Then:


Log[Sin[x]*Cos[y]] // expandLog



Log[Cos[y]] + Log[Sin[x]]


Log[a + b] + Log[c + d] // collectLog

Log[(a + b) (c + d)]

Have fun, Alexei



I can use PowerExapnd to expand a Log:

PowerExpand[Log[a b]]

Log[a] + Log[b]

How can I do the opposite, i.e. combine Log[a] + Log[b] into Log[a b]?

Thanks

Themis

-- 
Alexei Boulbitch, Dr. habil.
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