Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?

Question

Maybe this question is simple, but I really need some help. When we use the Maximum Likelihood Estimation(MLE) to estimate the parameters, why we always put the log() before the joint density? To use the sum in place of product? But why? The wikipedia said it will be convenient. Why? Thank you.

Answer 1

by using the log function our likelihood function is become more convenient and finding of its derivative is become more easy that's why we use log function. this is the only reason for using the log. in some cases derivative is not to easily calculate and after taking the log of likelihood function it's become simple. in the problem of MLE our aim is to maximize the likelihood function and after the applying log function there is no change in maximization.

Answer 2

There is one more (in addition to what was pointed out by ABHI and ABC) clear situation when taking log is useful: exponential family of distributions. Taking log helps you to get rid of unpleasant (in root finding process) exponents.