mIRC's options allow you to choose to log all channels and/or chats, none, or only those you choose.
You can:
-date them by day/week/month
- include the network name
- timestamp or not
-choose to have seperate folders for each network
- specify what folder/directory you want the logs to go (generally they are within the main mIRC folder).
-can log each channels, dcc chats, message/queries as well as status windows.

Some ppl choose to have all msgs/queries go to one window, altho most have a sep one for each person they are in private msg with so each person would have a log. Each channel has its own log. (assuming you have chosen to log)
You can opt to set this in mIRC's options, or by typing a command in the window you wish to log, or by setting it in the system menu for each window.

As a side note, it is very easy to create a fake log or edit one to show anything you want it to.