AQA A Level Biology

Revision Notes

4.4.2 Maths Skill: Using Logarithms When Investigating Bacteria

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

Yeast log scale graph, downloadable AS & A Level Biology revision notes

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

Logarithmic-Ph-Scale, downloadable AS & A Level Biology revision notes

Image showing the range of hydrogen ion concentrations within the pH scale.

Exam 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.

Author: Lára

Lára graduated from Oxford University in Biological Sciences and has now been a science tutor working in the UK for several years. Lára has a particular interest in the area of infectious disease and epidemiology, and enjoys creating original educational materials that develop confidence and facilitate learning.
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