Logarithmic Scales
What are logarithmic scales?
- Logarithmic scales are scales where intervals increase exponentially
- A normal scale might go 1, 2, 3, 4, ...
- A logarithmic scale might go 1, 10, 100, 1000, ...
- Sometimes we can keep the scales with constant intervals by changing the variables
- If the values of x increase exponentially: 1, 10, 100, 1000, ...
- Then you can use the variable log x instead which will have the scale: 1, 2, 3, 4, ...
- This will change the shape of the graph
- If the graph transforms to a straight line then it is easier to analyse
- Any base can be used for logarithmic scales
- The most common bases are 10 and e
Why do we use logarithmic scales?
- For variables that have a large range it can be difficult to plot on one graph
- Especially when a lot of the values are clustered in one region
- For example: populations of countries
- This can range from 800 to 1 450 000 000
- If we are interested in the rate of growth of a variable rather than the actual values then a logarithmic scale is useful