Logan is a city and county seat of Harrison County, Iowa, United States, along the Boyer River. The population was 1,397 at the 2020 census.

As of the census of 2010, there were 1,534 people, 595 households, and 397 families living in the city. The population density was 1,534.0 inhabitants per square mile (592.3/km2). There were 649 housing units at an average density of 649.0 per square mile (250.6/km2). The racial makeup of the city was 98.6% White, 0.1% African American, 0.1% Native American, 0.4% Asian, and 0.8% from two or more races. Hispanic or Latino of any race were 0.8% of the population.

There were 595 households, of which 35.0% had children under the age of 18 living with them, 54.1% were married couples living together, 9.1% had a female householder with no husband present, 3.5% had a male householder with no wife present, and 33.3% were non-families. 27.2% of all households were made up of individuals, and 14.1% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 3.07.

The median age in the city was 38.5 years. 26.9% of residents were under the age of 18; 6.1% were between the ages of 18 and 24; 25.5% were from 25 to 44; 24.9% were from 45 to 64; and 16.7% were 65 years of age or older. The gender makeup of the city was 48.7% male and 51.3% female.