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:

...
Apr 3 11:02:12 hostserver dnsmasq-dhcp[21458]: DHCPACK(eth0) 192.168.1.121 00:a2:89:5e:0a:69 PHONE1
Apr 3 11:02:26 hostserver dnsmasq-dhcp[21458]: DHCPACK(eth0) 192.168.1.182 00:a2:89:5e:9d:42 PHONE2
Apr 3 11:02:29 hostserver dnsmasq-dhcp[21458]: DHCPACK(eth0) 192.168.1.103 90:b1:1c:5d:86:d2 STATION-W3
...

You can filter it further down, if you know the hostname you are looking for:

cat /var/log/syslog | grep "DHCPACK" | grep "STATION-W3"

Will output just this:

Apr 3 11:02:29 hostserver dnsmasq-dhcp[21458]: DHCPACK(eth0) 192.168.1.103 90:b1:1c:5d:86:d2 STATION-W3

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