Solving Problems with Bounds on Linear Forms in Logarithms

Abstract

This expository paper explores the theory of linear forms in logarithms and its applications to Diophantine equations. We begin with foundational results on transcendental numbers, including Liouville's theorem and the Gelfond-Schneider theorem, before developing Baker's theory of linear forms in logarithms. The paper concludes with applications to Diophantine equations through the Baker-Davenport method, illustrating these techniques with concrete examples. The purpose of this paper is to provide a step-by-step understanding of this particular area of Mathematics, and was written as a part of Euler Circle's Independent Paper and Research Writing Program, in which the author studied the topic independently and wrote this paper over a period of 4 weeks.