Apartments For Rent Logan County Ohio . 64 apartments for rent in logan county, oh. 3 beds • 1 bath. Hocking College Campus Map Current Red Tide Florida Map from megantandonmiler.blogspot.com On average, section 8 housing choice vouchers pay logan county landlords $500 per month towards rent. There are 35 available rental. In addition to the rent cost, you need to also account for costs of basic utilities consisting of.