Why logarithmic scales are useful
Microorganisms can reproduce rapidly in culture, so their numbers may rise from relatively small values to very large values within only a few hours. A conventional linear scale can make data covering such a wide numerical range difficult to display clearly.
A logarithmic scale allows values spanning several orders of magnitude to fit onto the same graph. This makes it particularly useful for data involving large numbers of microorganisms.
Orders of magnitude
An order of magnitude is a tenfold change in quantity. On a base-10 logarithmic scale, moving through one order of magnitude means multiplying or dividing the value by 10.
| Change | Interpretation |
|---|---|
| 10 → 100 | One order of magnitude increase |
| 100 → 1000 | One order of magnitude increase |
| 1000 → 100 | One order of magnitude decrease |
Labels such as 1, 10, 100 and 1000 show that successive positions represent multiplication by the same factor rather than addition of the same numerical amount.
Interpreting microbial growth data
In the yeast-culture example, the population increases rapidly over ten hours and the number of cells spans a wide range. A logarithmic presentation allows both the smaller values near the start and the much larger later values to remain visible on one graph.
For this example, the cell-number measurements at each time interval are treated logarithmically for plotting. When reading the resulting scale, focus on the multiplicative progression of the values rather than treating neighbouring labels as equal numerical increases.
Another logarithmic scale: pH
The pH scale is logarithmic. Hydrogen ion concentration varies across a very large range between pH levels, giving another biological example of quantities that are conveniently represented logarithmically.
Exam Tip: Assessment focuses on reading results that use logarithmic scales and explaining why the scale is useful. Manual conversion of values into logarithms and construction of a logarithmic graph are not required. When interpreting an axis, look for change by a constant factor, such as ×10, rather than a constant numerical difference.