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Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?

• To: mathgroup at smc.vnet.net
• Subject: [mg81671] Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Mon, 1 Oct 2007 04:46:19 -0400 (EDT)

Hello,
This works as I would hope it would:

Simplify[Log[a^2] + Log[b^2] - Log[-2 b^2],
  Assumptions -> Element[a, Reals] && Element[b, Reals]]

It returns -Log[-2/a^2]

However, something a little more complicated:

Simplify[
Log[4] -
   - 2 Log[-2 ((R + x)^2 + y^2 + (z - zvar)^2)]
    +    2 Log[(R + x)^2 + y^2 + (z - zvar)^2]),
  Assumptions ->
{Element[zvar,Reals], Element[x,Reals],Element[y, Reals], Element[z, Reals}]

doesn't simplify. I can't see a way to do this, but brute force.

Any ideas?
Thanks,

W. Craig Carter

• Follow-Ups:
  • Re: Simplifying Log[a] + Log[expr_] - Log[2 expr_]: Brute force necessary?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>