Mathematica MATHEMATICA : Forcing Logarithms to Simplify

[Hepth]

How can I force :

A Log + A Log[c]

to simplify to A Log[b c]?

I tried, A,b,c all elements of reals, but it doesn't do it. (Assume everything is Real)
I know I can make some patterned rules but I'd rather have it be by default.

(i.e. : a_ Log[b_] + a_ Log[c_] :> a Log[b c])

 

[Bill Simpson]

Simplify[A Log + A Log[c], b > 0 && c > 0]

returns

A Log[b c]

 

[Hepth]

But what if b and c are not defined as non-zero positive? If b=-2 and c=-3 then shouldn't it come out ok? Or does that, by definition, involve choosing branch cuts.

Basically I'm doing this long integral, and its resulting in multiple logarithms that all end up, if I do it by hand, cancelling. I get something like:

(A) Log[-m1] + (-A) Log[-m2] + (-A) Log[m1*(2 E1-ma)] + (A) Log[m2*(2 E1-ma)

Which if you do by hand, ignoring the fact that m's are positive, you get A Log[1] which is zero. But Mathematica doesn't recognize this. Even the first two should simplify, but I think there's some options I need to choose correctly. I guess I'll start with making sure the m's are all defined as positive, as well as the E's.

 

[Bill Simpson]

When I Simplify your last expression while telling it that both m1 and m2 are positive or while telling it that both m1 and m2 are negative that is sufficient for it to return zero.

When you do it by hand are you explicitly including that every log of a negative real value includes an infinite set of c*2*i*Pi for a unique integer c each time or are you assuming that c==1 for every one of your Log?