Maths Skill: Using Logarithms When Investigating Bacteria
- Bacterial colonies can grow at rapid rates when in culture with very large numbers of bacteria produced within hours
- Dealing with the experimental data relating to large numbers of bacteria can be difficult when using traditional linear scales
- There is a wide range of very small and very large numbers
- This makes it hard to work out a suitable scale for the axes of graphs
- Logarithmic scales can be very useful when investigating bacteria
Using logarithms to deal with orders of magnitude
- Logarithmic scales allow for a wide range of values to be displayed on a single graph
- For example, yeast cells were grown in culture over several hours. The number of cells increased very rapidly from the original number of cells present
- The results from the experiment are shown in the graph below, using a log scale
- The number of yeast cells present at each time interval was converted to a logarithm before being plotted on the graph
- The log scale is easily identifiable as there are not equal intervals between the numbers on the y-axis
- The wide range of cell numbers fit easily onto the same scale
Image showing the number of yeast cells grown in culture over 10 hours, using a logarithmic scale
- The pH scale is logarithmic
- The concentration of hydrogen ions varies massively between each pH level
Image showing the range of hydrogen ion concentrations within the pH scale
Examiner Tip
You won’t be expected to convert values into logarithms or create a log scale graph in the exam. Instead you might be asked to interpret results that use logarithmic scales or explain the benefit of using one! Remember that graphs with a logarithmic scale have uneven intervals between values on one or more axes.
