Simplification of log and exp expressions

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 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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