This is how you can find out which IP is assigned to a computer using dnsmasq. Unless you've specified a different log for dnsmasq, the output will go into syslog (/var/log/syslog).
A quick way to isolate the requests, is by running this command:
cat /var/log/syslog | grep "DHCPACK"
This will produce a list of IPs assigned, with a MAC address and hostnames: