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Log[Product[]] expansion to Sum[Log[]]?

  • To: mathgroup at
  • Subject: [mg9160] Log[Product[]] expansion to Sum[Log[]]?
  • From: Julian Stoev <stoev at>
  • Date: Thu, 16 Oct 1997 03:38:01 -0400
  • Organization: Seoul National University, Republic of Korea
  • Sender: owner-wri-mathgroup at

Dear Group,
I want to simplify some expressions involving Product[] and Log[]. This
problem appears in calculation of Cramer-Rao lower bound of variation.
I want
Log[Product[SomeFunction[k],{k,1,N}]] to be transformed to 

Mathematica does not convert it in this form. I solved temporarilly the
problem by using 'brutal force" of rules, but I was wondering is there
more elegant way to do this, by defining some special properties of

The main problem appears to be that Log[a.b] is not Log[a]+Log[b]. I
know there were several discussions how to define variables real and
positive, but what about functions? I don' want to make big
modifications in default kernel behaviour.

Thank you!
Julian Stoev <j.h.stoev at>       - Ph. D. Student Intelligent
Information Processing Lab. - Seoul National University, Korea Work:
872-7283, Home: 880-4191          - !!!!! Use
REPLY-TO: or remove "SPAMREMOVER" in my address

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