When you visualize ratios, naturally, the reference point is 1. Let’s say you want to visualize the ratios between a and b.
Let $a = 10$ and $b = \frac{1}{10}$.
Then, we have
$$\frac{a}{b} = \frac{10}{\frac{1}{10}} = 100 \tag{1}\label{eq1}$$
and
$$\frac{b}{a} = \frac{\frac{1}{10}}{10} = \frac{1}{100} \tag{2}\label{eq2}$$
If you do not use log scale, then the difference between 1 and $\frac{a}{b}$ is much larger than the difference between 1 and $\frac{b}{a}$. However, intuitively, the two differences should be the same, right? Using log scale solves this issue.
Last modified on 2022-04-26