There are two logs per TCG: one to log various TCG activities, and another to log trades.

Your logs have a maximum length of approximately 4,294,967,295 or 4GB characters (also depends on your server). However, very long logs can potentially cause things to load slowly, so you should ARCHIVE them periodically. There is an archive button for your logs here, which will move all current logs to archived logs.

Keep in mind that these archived logs have the same limit as your current logs, and take up the same amount of space in your database. The benefit is that they are never called up by the script, except if you should choose to edit them or display them on your trade post. You may also prefer to just save the archives on your own computer.