In mathematics, a logarithm (or simply known as a log) is the exponent that is required to produce a number, based on the logarithm’s base. In science, it is sometimes beneficial to use a logarithmic scale for figures and plots by converting both axes to the same length-scale, allowing for better perception of what the figure or plot implies. Converting data from a logarithmic scale to a linear scale is a simple process and requires very little mathematical skill.

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When collecting the data points from a figure, be extra mindful of the x- and y- scales. The values listed on the scale are not linear.

Determine what the base of the logarithm is. Look for the number to the right of the word “log” in smaller subscript. Be warned that the base of a logarithm is not the value to the right of the word “log” in standard size. If a base is not listed, then it can always be assumed that the base is 10.

If the word “log” is not present, but the word “ln” is, then the base is the letter “e.” “ln” in this case is short for “natural logarithm” which is the same thing as a logarithm with base “e.”

Collect the data points from the figure in logarithmic scale. This can be done by taking a ruler and noting the x- and y- coordinates of each data point.

Convert from a logarithmic scale to a linear scale by raising the base of the logarithm to the power of each data point collected. The new values calculated are now the same data, but in the linear scale.

For example, say the points (1, 2) and (2, 3) in logarithmic scale were collected, and it was determined that the base of the logarithm was 10. To convert from logarithmic scale to linear scale, raise the base, value of 10, to the power of each x- and y- data point. The first ordered pair would be 10 raised to the first and second powers, producing values of 10 and 100, such that the ordered pair in linear scale is (10, 100). The second ordered pair would be 10 raised to the second, and 10 raised to the third power, resulting in (100, 1,000).

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