Semilog graph

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The lin-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=x (green), y=10^x(red), y=log(x) (blue).

The log-lin type of a semi-log graph, defined by a logarithmic scale on the y axis, and a linear scale on the x axis. Plotted lines are: y=x (green), y=10^x(red), y=log(x) (blue).

In science and engineering, a semi-log graph or semi-log plot is a way of visualizing data that are changing with an exponential relationship. One axis is plotted on a logarithmic scale. All functions of the form $y = λ a γ x$ form straight lines, since taking logs of both sides is equal to

log a y = γ x + log a λ

This can easily be seen as a line in slope-intercept form with $γ$ as slope, $log a λ$ as the y-intercept. To facilitate use with logarithmic tables, one usually takes logs to base 10 or e:

log(y) = (γlog(a)) x + log(λ)

The term log-lin is used to describe a semi-log plot with a logarithmic scale on the y axis, and a linear scale on the x axis. Likewise, a lin-log graph uses a logarithmic scale on the x axis, and a linear scale on the y axis.

A log-log graph uses the logarithmic scale for both axes, and hence is not a semi-log graph.