I would like to mark down the reasons that I found helpful for intuitive understandings.
First reason: for the sake of familiarity.
Distributions whose variances stay the same across all the data is the one we are most familiar with and we are happy to deal with! But some variables do not come with the same variance across the data. Ratios are one of those.
Below is a plot of random ratios. As you can see, the graph grows slow until the point of 1 or 2, then grows much faster after that. For such kind of variable, we cannot fit distributions we’re familiar with, such as normal distribution, exponential distribution or gamma distribution.
But if we take log of each ratio and plot the data again (below), we can see now the graph grows steadily across the data. Linear regression is applicable now (if necessary).
Second reason: for the convenience of calculation.
We all learned that log(X/Y) and log(X*Y) can be written as the following:
log(X/Y) =log(X) — log(Y)
log(X*Y) =log(X)+log(Y)
By taking log, we can convert multiplication or deviation problem into addition or subtraction problem. I believe most people would find addition and subtraction easier to calculate!
