Semi-log plot

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 = 10x (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 = 10x (red), y = x (green), y = log(x) (blue).

In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale. It is useful for data with exponential relationships, where one variable covers a large range of values.[1]

All equations of the form form straight lines when plotted semi-logarithmically, since taking logs of both sides gives

This is a line with slope and vertical intercept. The logarithmic scale is usually labeled in base 10; occasionally in base 2:

A log–linear (sometimes log–lin) plot has the logarithmic scale on the y-axis, and a linear scale on the x-axis; a linear–log (sometimes lin–log) is the opposite. The naming is output–input (yx), the opposite order from (x, y).

On a semi-log plot the spacing of the scale on the y-axis (or x-axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on linear scales. A log–log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.

  1. ^ (1) Bourne, M. "Graphs on Logarithmic and Semi-Logarithmic Paper". Interactive Mathematics. www.intmath.com. Archived from the original on August 6, 2021. Retrieved October 26, 2021.
    (2) Bourne, Murray (January 25, 2007). "Interesting semi-logarithmic graph – YouTube Traffic Rank". SquareCirclez: The IntMath blog. www.intmath.com. Archived from the original on February 26, 2021. Retrieved October 26, 2021.