Over the first century and a half of their discovery, logarithms were seen and understood in a variety of ways. Depending on the mathematical beliefs of an author, they could choose to introduce logarithms as a geometric-mechanical object, or as an index of a geometric progression, or through an exponential equation. The choice of introduction then influenced how their reader viewed and used logarithms, and has implications for teachers today as they attempt to explain this topic. In looking over the works of three authors, Colin MacLaurin, William Frend, and George Peacock, we can see logarithms displayed in three different ways. In combining these presentations with our modern understanding of logarithms as a number, an operation, and a function, we can choose parts of the text that could help current students make sense of a difficult concept. Keywords: history, mathematicians, Cambridge, logarithms, textbook analysis