Dimensional analysis and logarithmic functions

Abstract

Students are often confused by units when dealing with a logarithmic function. This is frequently dealt with by stating that the function gives a unitless result. Though correct, it does not address the deeper question of why the logarithm is unitless and how a graphical analysis involving logarithms can lead to unitless results that depend on the original data’s units. This paper explains this by considering the logarithm as a transcendental function and how that relates to the determination of units.