Semi-log plot

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. 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 log a ⁡ y = γ x + log a ⁡ λ . {\displaystyle \log _{a}y=\gamma x+\log _{a}\lambda .} 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: log ⁡ ( y ) = ( γ log ⁡ ( a ) ) x + log ⁡ ( λ ) . {\displaystyle \log(y)=(\gamma \log(a))x+\log(\lambda ).} 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 (y–x), 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.