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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, or to zoom in and visualize that - what seems to be a straight line in the beginning - is in fact the slow start of a logarithmic curve that is about to spike and changes are much bigger than thought initially.
All equations of the form y = λ a γ x {\displaystyle y=\lambda a^{\gamma x}} form straight lines when plotted semi-logarithmically, since taking logs of both sides gives
This is a line with slope γ {\displaystyle \gamma } and log a λ {\displaystyle \log _{a}\lambda } vertical intercept. The logarithmic scale is usually labeled in base 10; occasionally in base 2:
A log–linear plot has the logarithmic scale on the y-axis, and a linear scale on the x-axis; a linear-log is the opposite. The naming is output-input , the opposite order from.