As the title suggested, I want to know why people often use log likelihood function, instead of likelihood function by itself. What I know, is that, if $\hat{\theta}$ is the maximum of a likelihood function $f(\theta; \mathbf{x})$, then it is also the maximum of $g(\theta) := \log (f(\theta; \mathbf{x}))$. Are there some other reasons why we are interested in $g$ instead of $f$?
What are some of the disadvantages of working with log likelihood function instead of likelihood function?
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statistics