Logarithms (Zambak)

This book constitutes a high-school course in exponential and logarithmic functions. Since the concepts of logarithm and logarithmic function are new to most students at this level, the material assumes no prior knowledge of the subject, although students should be familiar with real numbers and their properties, with exponents and their properties, and with linear and quadratic functions and their graphs. In particular, students should have studied the Numbers and Functions modules in the Zambak Modular System mathematics series before beginning this book.
The book is divided into three chapters, structured as follows:
• Chapter I deals with exponents and exponential functions. It begins with a review of the basic properties of exponents, followed by an introduction to exponential functions. An optional third section discusses the graphs of exponential functions and some simple variations, and the fourth section looks at applications of exponential functions.
• Chapter 2 introduces logarithms and logarithmic functions and their properties. The third section (again optional) looks at the graphs of logarithmic functions and some standard transformations. The fourth section covers three applications of logarithmic functions in the real world, namely the Richter scale, the pH scale and the decibel scale.
• Chapter 3 looks at equations and inequalities, building on the material covered in the first two chapters. The text presents exponential equations and inequalities in the first section, and moves on to logarithmic equations and inequalities in the second. The third and final section looks at systems of equations and inequalities.
This book has been designed to be an effective teaching aid and includes all of the features of the Zambak Modular System mathematics series.