### Introduction

In this Section we employ our knowledge of logarithms to simplify plotting the relation between one variable and another. In particular we consider those situations in which one of the variables requires scaling because the range of its data values is very large in comparison to the range of the other variable.

We will only employ logarithms to base 10. To aid the plotting process we explain how log-linear graph paper is used. Unlike ordinary graph paper, one of the axes is scaled using logarithmic values instead of the values themselves. By this process, values which range from (say) 1 to 1,000,000 are scaled down to range over the values 0 to 6. We do not discuss log-log graphs, in which both data sets require scaling, as the reader will easily be able to adapt the technique described here to those situations.

#### Prerequisites

• be familiar with the laws of logarithms
• have knowledge of logarithms to base 10
• be able to solve equations involving logarithms

#### Learning Outcomes

• decide when to use log-linear graph paper
• use log-linear graph paper to analyse functions of the form $y=k{a}^{px}$