### Introduction

In this Section we introduce the logarithm: ${log}_{a}b$ . The operation of taking a logarithm essentially reverses the operation of raising a number to a power. We will formulate the basic laws satisfied by all logarithms and learn how to manipulate expressions involving logarithms. We shall see that to every law of indices there is an equivalent law of logarithms. Although logarithms to any positive base are defined it is common practice to employ only two kinds of logarithms: logs to base $10$ and logs to base $\text{e}$ .

#### Prerequisites

- have a knowledge of exponents and of the laws of indices

#### Learning Outcomes

- invert $b={a}^{n}$ using logarithms
- simplify expressions involving logarithms
- change bases in logarithms

#### Contents

1 Logarithms2 Simplifying expressions involving logarithms

3 Logs to base 10 and natural logs

4 Changing base in logarithms