# Chapter one

Mathematical skills

## Section three: Exponentials and logarithms

This chapter is on the theme of supporting mathematics that are needed for engineering problem solving, analysis, design and evaluation.

The videos in this section give an introduction to exponential and logarithm functions and their key attributes.

It is assumed that students have been introduced to these functions before, albeit briefly. Therefore, the focus is more on identifying and understanding the key properties that will be used in engineering problem solving.

### 1. Introduction to exponentials

A rapid review of indices or powers as a lead into the definition of an exponential function as a special case of a power function.

A talk through video is on YouTube.

### 2. Properties of exponentials

This video derives and explains the key properties of exponential functions such as key values, asymptotic behaviour, sketches and monotonicity.

A talk through video is on YouTube.

### 3. Definition of logarithms

This video introduces logarithms as the inverse function of an exponential. The video uses this definition to derive and demonstrate core properties (or rules) of logs which students will need for common problem solving.

A talk through video is on YouTube.

### 4. Algebra with logarithms

A number of worked examples demonstrating the use of the rules and the importance of estimation skills when using logarithms.

A talk through video is on YouTube.

### 5. Domain and range

As exponential and logarithm are inverse functions, their range and domains must be linked. This brief video gives an illustration of this.

A talk through video is on YouTube.

### 6. Miscellaneous

This video highlights a few engineering problem solving skills linked to logarithms. How do we identify exponential behaviour in a noisy signal and what is logarithmic graph paper?

A talk through video is on YouTube.