This is how I've always taught logarithms to students I've tutored. I photocopy a table of various powers of ten, we use it in all sorts of ways to solve proble

This is how I've always taught logarithms to students I've tutored. I photocopy a table of various powers of ten, we use it in all sorts of ways to solve problems, and then I sneakily present an "inverse power" problem where they need to make the lookup backwards. Almost every student gets it right away, and then I tell them looking up things backwards in the power table is called taking a logarithm.