Simplification of log and exp expressions

Robert Dodier [05/09/03 19:57 -0700]:
> Hello,
> 
> I want to convert expressions such as 
> exp(5 .a).exp(2 .a).exp(z.a) to exp((7+z).a),
> but Maxima (5.9.0) doesn't seem to do that.
> I've tried some functions (radcan, simplify,
> expand, contract...) and I've read the man 
> pages and searched the mailing list archives,
> but I've come up empty-handed. 
> 

I am not sure I understand what exactly did not work for you. Here
is what I tried:

(C1) exp(5*a)*exp(2*a)*exp(z*a);

                                    a z + 7 a
(D1)                              %E
(C2) factor(log(d1));

(D2)                              a(z+7)
(C3) exp(D2);
                                    a (z + 7)
(D3)                              %E
	
	As Richard pointed out in his reply to your question, x . y is
	different from x*y.

Hope this helps.
Milan

> I was thinking that I could try taking the 
> logarithm and then simplifying the resulting
> linear combination, but log of the above 
> expression has no action -- the output is just
> LOG(%E^(5*a) . %E^(2*a) . %E^(z . a)).
> 
> How can I tell Maxima to combine exponents?
> 
> As a separate question, how can I tell Maxima
> that log converts multiplication to addition,
> and exp converts addition to multiplication?
> Maxima seems to already know that log(exp(a)) is
> just a, so if I could get the log of the product
> changed into sum of the logs, it seems the 
> simplification could proceed from there.
> 
> Thanks very much for any advice you might have.
> 
> Robert Dodier
> 
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