|Well the modem/router may have logging capabilities in which case there is nothing you can do to prevent such a log if you do not have router admin access.|
My old netgear router kept & provided complete logs of all URLs accessed by each client system. The D-Link I now use logs only DHCP stats. No URL data is logged. You will need to read the user manual for the modem/router to see what logging capability it has.
As far as your personal system privacy goes you need to maintain a software firewall and ensure file & printer sharing is turned off.
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