I thought the Logitech cordless range used wireless, not bluetooth, so I am puzzled by the BT 'dongle' you describe. My (more basic) L cordless combo connects via a mouse charging station to a USB port. What do the instructions say?
"Out of the box, you will get the Logitech MX3200 keyboard itself, black Logitech MX600 cordless laser mouse, SecureConnect RF (Radio Frequency) mini receiver, receiver stand, Logitech product brochure, driver CD and 6 Duracell AA batteries in individual sets of two."
No mention of Bluetooth/dongle???
"Setting up the Logitech Cordless Desktop MX 3100 was no more difficult than setting up any other cordless keyboard and mouse combo - just plug the wireless receiver into any free USB port, install the supplied Logitech software, then hit the "Connect" buttons on mouse keyboard and wireless receiver. Before you start using the system on your favorite games or apps you should sit the MX 1000 laser mouse on the charging base to fully juice up the battery. "