Will a cable modem keep a list of recently visited websites like a dsl modem will?”
I’ve got one of the best cable modems around, the Motorola Surfboard 5120. It supposedly has one of the best diagnostics available. Its log lists connection and configuration settings, but not which websites were visited. However, your firewall software may have this information. To connect to most if not all cable modems, you need to enter this IP address in your web browser: http://192.168.100.1/ From there I can check the modem’s status, signal levels, its MAC address and the addresses of the computers hooked up to it, connection logs, and some configuration settings, though I don’t think as many as are possible with a DSL modem. I hope this answers your question!