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Logarithmic scale

The logarithmic scale is a nonlinear scale that is used when measurements differ by several orders of magnitude.

Have a look at following three functions plotted on a linear scale on the left and a logarithmic scale on the right. Notice how the exponential function, the first function in the right graph, becomes a straight line on the logarithmic scale.

Two graphs. Legend reads that f bracket x close bracket equals different colors. 10 to the power of x is in red, x is in green and lawn x is in blue. Left graph is a linear scale on the y-axis and x-axis. Three colored lines on the graph display positive exponential growth in red, linear growth in green and negative exponential growth in blue. Right graph is a logarithmic scale on the y-axis and linear on the x-axis. Three lines display a linear line in red, and two negative exponential growths in green and blue. The green line is above the blue.

Figure 1: Two graphs with linear x-axes showing three functions, f(x); a positive exponential function (red), a linear function (pale blue), and a negative exponential function (blue). The left graph has a linear y-axis and the right graph has a logarithmic y-axis.

Common uses for a logarithmic scale include earthquake strength, sound loudness, light intensity, growth curves, and pH of solutions.

Check out the logarithmic laws to learn how to calculate with logarithms.

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Article
Logarithmic laws