D. B. A. Epstein, V. Markovic, The Logarithmic Spiral: A Counterexample to the K = 2 Conjecture, Annals of Mathematics, Second Series, Vol. 161, No. 2 (Mar., 2005 ...

There is a simple non-algebraical and very clear explanation of logarithms; then the real object of the book, an explanation of the slide-rule, follows.