I just inherited two slide rules from my grandfather-in-law, one wood with smooth action despite nearly a century without use.1 (I used a K+E slide rule myself as an undergraduate in the 1970's.) It struck me that the conversion of multiplication/division to addition/subtraction via the logarithmically ruled markings might serve as a memorable physical instantiation of $\log ab = \log a + \log b$, or $x^a x^b = x^{a+b}$, etc. One of the slide rules came with instructions on how to take the $n$-th root of a number!
I've never taught logarithms, but I wonder if those who have, ever bring in to the classroom slide rules as "props"?
1Lawrence Engineering Service, Peru, Indiana.