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
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Alexei Boulbitch, Dr. habil.
Senior Scientist
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