Semi-log plot

In science and engineering, a semi-log graph or semi-log plot is a way of visualizing data that are related according to an exponential relationship. One axis is plotted on a logarithmic scale. This kind of plot is useful when one of the variables being plotted covers a large range of values and the other has only a restricted range – the advantage being that it can bring out features in the data that would not easily be seen if both variables had been plotted linearly.

All equations of the form ${\displaystyle y=\lambda a^{\gamma x}}$ form straight lines when plotted semi-logarithmically, since taking logs of both sides gives

This can easily be seen as a line in slope-intercept form with ${\displaystyle \gamma }$ as the slope and ${\displaystyle \log _{a}\lambda }$ as the vertical intercept. To facilitate use with logarithmic tables, one usually takes logs to base 10 or e, or sometimes base 2:

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