Bacterial populations can grow from a few hundred cells to billions in a day. On a normal (linear) axis, the early numbers would be squashed against zero and the later ones would run off the graph. Microbiologists therefore plot the logarithm of the number of cells.The logarithm to base 10 (log10) of a number is the power to which 10 must be raised to give that number:log10 1000 = 3, because 103 = 1000 So log10 106 = 6, and log10 (5 × 106) = 6.70. On a log scale, each step of 1 unit means the number is 10 times larger, so a scale from 2 to 9 covers numbers from one hundred to one billion.
There are two ways to draw this: plot log10 (number of cells) on an ordinary y-axis, or plot the raw numbers on semi-log graph paper, where the y-axis is already spaced logarithmically and time stays on a normal x-axis.A big advantage is that the exponential (log) phase becomes a straight line, because each doubling adds the same amount (log10 2 = 0.301) to log10 N. This makes it easy to see where the log phase starts and ends, and to measure its gradient.To convert back, take the antilog: if log10 N = 4.5, then N = 104.5 = 3.16 × 104 cells.Worked example: a culture grows from 103 to 108 cells. On the log scale it rises from 3 to 8, an increase of 5, which means 105 (100 000) times more cells.
There are two ways to draw this: plot log10 (number of cells) on an ordinary y-axis, or plot the raw numbers on semi-log graph paper, where the y-axis is already spaced logarithmically and time stays on a normal x-axis.A big advantage is that the exponential (log) phase becomes a straight line, because each doubling adds the same amount (log10 2 = 0.301) to log10 N. This makes it easy to see where the log phase starts and ends, and to measure its gradient.To convert back, take the antilog: if log10 N = 4.5, then N = 104.5 = 3.16 × 104 cells.Worked example: a culture grows from 103 to 108 cells. On the log scale it rises from 3 to 8, an increase of 5, which means 105 (100 000) times more cells.