Why do we see so many logarithms in machine learning (log)

If you jump into the loss functions in machine learning algorithms, you might encounter many logarithms. Why?

1. What is a logarithm
2. The traits of the logarithm
3. Why do we use it in machine learning

1. What is a logarithm

A logarithm is the inverse of an exponential.

a^x = y
log_a(y) = x

x means how many times a multiplied by itself. A common one is a =10.

10^2 = 100
log_10(100) = 2

2. The traits of the logarithm

(1) It turns multiplication into addition

One rule of logs is that log(A*B*C) = log(A) + log(B) + log(C)
log{(2%)*(3%)*(4%)}= log(2%) + log(3%) + log(4%)

The output of (2%)*(3%)*(4%) is really small 0.000024, on the other hand, log(2%) + log(3%) + log(4%) is (-1.699) + (-1.523) +(-1.398) = -4.62

(2) It makes the exponential relationships easier to interpret

Raw data and Base-10 log of total U.S. COVID-19 case count [1]