These logs are very important in security incidents and I would not recommend trying to limit what is written to them.
You have a couple options to go through them; if you're going through them "after the fact" you can simply use the grep command to view entries only from your IP. Otherwise if you want to watch in "real time" you can simply pipe the tail -f command through a grep while logged into SSH such as:
Code:
# tail -f /usr/local/cpanel/logs/access_log | grep 123.123.123.123
This will cause only lines containing your IP to be output to the terminal until you kill the command with ctrl-c