The county auditor, at the time of making the assessment of real property subject to taxation, shall enter in a separate list pertinent descriptions of all burying grounds, public schoolhouses, houses used exclusively for public worship, institutions of purely public charity, real property used exclusively for a home for the aged, as defined in section 5701.13 of the Revised Code, public buildings and property used exclusively for any public purpose, and any other property, with the lot or tract of land on which such house, institution, public building, or other property is situated, and which have been exempted from taxation by the tax commissioner or auditor under section 5715.27 of the Revised Code or by the housing officer under section 3735.67 of the Revised Code. The auditor shall value such houses, buildings, property, and lots and tracts of land at their taxable value in the same manner as the auditor is required to value other real property, designating in each case the township, municipal corporation, and number of the school district, or the name or designation of the school, religious society, or institution to which each house, lot, or tract belongs. If such property is held and used for other public purposes, the auditor shall state by whom or how it is held.