The Web Archive is a very useful tool. I suggest bookmarking it and checking it periodically.
Do a search for “logan county” illinois. Write it just like that including the quotes. Since the last time I checked they have the 1860 and 1870 census. They are long downloads since they put the entire state in one file but it is worth it. They also have some of the old histories, maybe one you are looking for.
It is free.