Armendariz, Efraim P.2010-06-042017-05-112010-06-042017-05-112009-08August 200http://hdl.handle.net/2152/ETD-UT-2009-08-195textThis paper outlines the evolution of the logarithm from the days of Archimedes to the logarithm now used in modern mathematics. Each type of logarithm developed had its particular usefulness. The Archimedean logarithm helped astronomers by drastically shortening the time it took to multiply large numbers, while Napier’s logarithm could be used as a tool to solve velocity problems. With the discovery of the number e, the natural logarithm was developed. Due to the frequent use of e, many of the properties of logarithms were defined to work nicely for the natural logarithm to make calculations easier. This paper will explain the proofs and connections of such properties in a way that could be presented in a calculus class.application/pdfengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.natural logarithmlogarithmthesis