mIRC has a logging feature that is on by default, so you should be able to see the log of your channel by typing //run $logdir in any mIRC's editbox, it will open the directory where mirc store the logs
#mircscripting @ irc.swiftirc.net == the best mIRC help channel
Note that if you have logging disabled, you will not be able to retrieve the log. However, *someone* in the channel likely has logging enabled and you might be able to get the log from them.