Mathematical skills - Exponentials and Logarithms

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.

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

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.

Derives and explains the key properties of exponential functions such as key values, asymptotic behaviour, sketches, monotonicity and so on.

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

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