What president was known as log cabin president?

Lincoln , Fillmore, Buchanan and Garfield were definitely born in log cabins. The exact birthplace of Jackson and Taylor is not known. Jackson is likely to have been born in a log cabin- Taylor less likely but quite possibly. Andrew Johnson was born in a small log house. Grant was born in a very small house that was partially made of logs, I think. William Henry Harrison may have lived in a log house for awhile when he first went to Indiana.