# Why You Want to Use Log Scale When Visualizing Ratios?

Hongtao Hao / 2021-10-09

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.