Cut the /var/log/syslog file using the comma (',') as the delimiter and take the field which is the result of the awk command that generates a random number between 1 and 7.
cut -d',' -f`awk -v min=1 -v max=7 'BEGIN{srand(); print int(min+rand()*(max-min+1))'` /var/log/syslog