Hopefully you can find someone that has immediate access to do a search for you. If not you can go to familysearch.org and order the microfilm. I have ordered these Tax Lists myself . You will have to find a Family History Library near you (Church of Latter Day Saints - Mormons). Almost all of them have a Genealogy library. You order the microfilm on-line and it is sent to your local Mormon church genealogy library. Some churches may still order for you.
Search for: United States, Kentucky, Wayne - Taxation ( 2 )
Tax books, 1801-1875
These are the two microfilm you will look for:
Tax books 1826-1830, 1833-1845 film no. 8270
Tax books 1846, 1848-1860 film no. 8271
Also many State Libraries may have them - contact your local state library.