Logan is a village in Quay County, New Mexico, United States. The population was 1,042 at the 2010 census. Logan was born when the …Logan is a village in Quay County, New Mexico, United States. The population was 1,042 at the 2010 census. Logan was born when the Chicago, Rock Island and Pacific Railroad constructed a bridge over the Canadian River. Eugene Logan was a well-known Texas Ranger who came to work on the bridge.