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.

• $log\left(1250\right)\approx 3.10$ so $1250\approx {10}^{3.10}$.
You therefore plot $1250$ exactly $3.10$ units above ${10}^{0}$, so between ${10}^{3}$ and ${10}^{4}$.

• $log\left(0.074\right)\approx -1.13$ so $0.074\approx {10}^{-1.13}$.
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.