In order to log all lines of your modem ``conversation'', you must enable the following:
set log +connect
This will make ppp(8) log everything up until the last requested ``expect'' string.
If you wish to see your connect speed and are using PAP or CHAP (and therefore do not have anything to ``chat'' after the CONNECT in the dial script - no set login script), you must make sure that you instruct ppp(8) to ``expect'' the whole CONNECT line, something like this:
set dial "ABORT BUSY ABORT NO\\sCARRIER TIMEOUT 4 \ \"\" ATZ OK-ATZ-OK ATDT\\T TIMEOUT 60 CONNECT \\c \\n"
Here, we get our CONNECT, send nothing, then expect a line-feed, forcing ppp(8) to read the whole CONNECT response.