Why log likelihoods are additive and !log likelihoods are multiplicative

Question

Reading accepted answer for Why we consider log likelihood instead of Likelihood in Gaussian Distribution by user jokek

states that total likelihood is product of likelihoods. If apply log to likelihoods then total likelihood is sum instead of product. Why applying log function to likelihoods change computing total likelihood from product to sum ? What is the intuition behind this ?

Answer 1

It's just a property of logarithms: $\log uv = \log u + \log v$.

Answer 2

Simply because $\log (ab)=\log(a)+\log(b)$.