You can put a rule with a LOG target into the NAT table with the same conditions as the DNAT rule. eg
/sbin/iptables -t nat -A PREROUTING -p tcp -i eth0 --dport 22022 -j LOG --log-prefix PortForward:
Put this just before the corresponding DNAT rule, and you will get stuff in the /var/log/messages file by default. To put them into another file, you have limited choices with the standard syslog facilities. A better scheme uses syslog-ng, which gives you more flexibility in sorting and routing log messages.