# How to Read a Semi-Log Graph

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In science, semi-log graphs are frequently used when plotting exponential quantities. For instance, you might notice that a semi-log graph is used to track the growth of a bacterial population, since the greater in magnitude a bacterial population becomes the faster the bacteria will multiply. Semi-log graphs are quite similar in concept to graphs made on Cartesian paper, except that the y-axis of a semi-log graph consists of different cycles of 10 (0.01 to 0.1, 0.1 to 10, 10 to 100, 100 to 1000, etc). After you master reading the y-axis of a semi-log graph, you will be able to interpret the graph.

Use the legend of the graph to determine what both the x-axis and y-axis are meant to illustrate. For instance, when working with a bacterial population, the x-axis may denote time, while the y-axis may denote the magnitude of the population. The legend will be useful to you as you interpret your graphs.

Determine a point's x-coordinate, by determining its corresponding value directly downward on the x-axis.

Use a ruler to determine where a point stands on the y-axis. Each cycle of 10, on semi-log graph paper, is divided into 10 increments. For instance, between 0.1 and 1, there are increments denoting 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. Between 1 and 10, there are increments of 2, 3, 4, 5, 6, 7, 8, and 9. Locate the particular increment corresponding to your point. If your point is located in between two increments, then you can average the two. For instance, if it is between 0.2 and 0.3, then the point is 0.25.

Write the coordinates of all your points, using the procedures outlined in Steps 2 and 3.