Re: combining Log[] terms

*To*: mathgroup at smc.vnet.net*Subject*: [mg30506] Re: combining Log[] terms*From*: "Souvik Banerjee" <s-banerjee at nwu.edu>*Date*: Fri, 24 Aug 2001 04:06:07 -0400 (EDT)*Organization*: Northwestern University, Evanston, IL, US*References*: <9m281v$h28$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The result is not true when one of a or b is negative. For example, Log[-a], where a>0 can be written as Log[-1] + Log[a] = i Pi + Log[a] (using DeMoivre's theorem). Hence, Log[-a] - Log[b] = i Pi + Log[a/b]. However, if both a and b are negative then the i Pi term cancels and you get the same result. Hence use either: Simplify[Log[a] - Log[b], {b > 0, a > 0}] to get Log[a/b]. or Simplify[Log[a] - Log[b], {b < 0, a < 0}] to get Log[a/b]. -Souvik > Is there a function that combines terms like > > Log[a] - Log[b] > > to > > Log[a/b]? > > I couldn't find anything so far in the documentation regarding the > Log[] function, only some references to Collect[], which does > something similar to what I want for powers of a given expression. > > Thanks already for you help, > > nick >