Logarithmic functions > Logarithmic scales
12345Logarithmic scales

Theory

In a logarithmic scale you have the powers of 10 at equal distances from each other. This means that you can plot both very small and very large numbers.
Using the base 10-logarithm ([LOG] on your calculator) you can very quickly identify which power of 10 belongs to a given number.

  • log ( 1250 ) 3.10 so 1250 10 3.10 .
    You therefore plot 1250 exactly 3.10 units above 10 0 , so between 10 3 and 10 4 .

  • log ( 0.074 ) -1.13 so 0.074 10 -1.13 .
    You therefore plot 0.074 exactly 1.13 units below 10 0 , so between 10 -1 and 10 -2 .

If you use a logarithmic scale on your vertical axis and a linear scale on you horizontal axis, then the graph of an exponential function turns into a straight line. In Excel it is very easy to make graphs with logarithmic scales. There is also a special semi-logarithmic paper.

Since every straight line on semi-logarithmic paper is the graph of an exponential function, you can use this paper to check if there is an exponential relationship between two variables, and to set up the corresponding formula.

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