### Introduction

In this Section we consider the logarithmic function $y={log}_{a}x$ and examine its important characteristics. We see that this function is only defined if $x$ is a positive number. We also see that the $log$ function is the inverse of the exponential function and vice versa. We show, through numerous examples, how equations involving logarithms and exponentials can be solved.

#### Prerequisites

- have knowledge of inverse functions
- have knowledge of the laws of logarithms and of the laws of indices
- be able to solve quadratic equations

#### Learning Outcomes

- explain the relation between the logarithm and the exponential function
- solve equations involving exponentials and logarithms

#### Contents

1 The logarithmic function2 Solving equations involving logarithms and exponentials

3 Engineering Example 1

3.1 Arrheniusâ€™ law