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