There are 4 US Post Offices in Logan County serving a total of 27,295 residents equating to 6,824 residents per post office. It's estimated that approximately 43,566 packages are handled across the 4 county post offices annually. Logan County is a county located in the southwest Pennyroyal area of the U.S. state of Kentucky. As of the 2010 census, the population was 26,835. Its county seat is Russellville."