Semi-log plot

It is useful for data with exponential relationships, where one variable covers a large range of values.

In other words, F is proportional to the logarithm of x times the slope of the straight line of its lin–log graph, plus a constant.

Therefore, the logs can be inverted to find: or This can be generalized for any point, instead of just F1: In physics and chemistry, a plot of logarithm of pressure against temperature can be used to illustrate the various phases of a substance, as in the following for water: While ten is the most common base, there are times when other bases are more appropriate, as in this example:[further explanation needed] Notice that while the horizontal (time) axis is linear, with the dates evenly spaced, the vertical (cases) axis is logarithmic, with the evenly spaced divisions being labelled with successive powers of two.

The semi-log plot makes it easier to see when the infection has stopped spreading at its maximum rate, i.e. the straight line on this exponential plot, and starts to curve to indicate a slower rate.

This might indicate that some form of mitigation action is working, e.g. social distancing.

In biology and biological engineering, the change in numbers of microbes due to asexual reproduction and nutrient exhaustion is commonly illustrated by a semi-log plot.

Time is usually the independent axis, with the logarithm of the number or mass of bacteria or other microbe as the dependent variable.

The log–linear type of a semi-log graph, defined by a logarithmic scale on the y -axis (vertical), and a linear scale on the x -axis (horizontal). Plotted lines are: y = 10 x (red), y = x (green), y = log( x ) (blue).
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log( x ) (blue).
log–linear pressure–temperature phase diagram of water. The Roman numerals indicate various ice phases .
A semi-logarithmic plot of cases and deaths in the 2009 outbreak of influenza A (H1N1) .
Bacterial growth curve