Transaction logs are written books that are recieved when your item is sold in the grand exchange. At the moment of retrieving these books from your mailbox you recieve the money from the buyer. When you open the book you find information about who baught the item, how much it was sold for and what the item was.
They have no use in any skill, event or quest.
Currently the only way to get rid of these books is by throwing them onto the ground and waiting for them to despawn.