Select Page
HSC Together > Year11 > Relationship between Logarithms and Exponentials

# Relationship between Logarithms and Exponentials

### What is the relationship between logarithms and exponentials?

In this post, we recognise and use the inverse relationship between logarithms and exponentials, as a part of the Prelim Maths Advanced course under the topic Exponential and Logarithmic Functions and sub-part Introducing Logarithms. We learn to understand the relationship between logarithms and exponentials and use the fact that log_{a}a^{x} = x for all real x , and a^{log_{a}x}=x for all x>0 .

### How do I convert between exponential and logarithmic form?

The video below covers the relationship between logarithms and exponentials and how you are able to convert from exponentials to logarithms and vice versa.

### Comparing exponential and logarithmic functions

This video compares the graphical properties of an exponential and logarithmic function, listing their similarities and relationship.