I am reading Gaussian Distribution from a machine learning book. It states that -

We shall determine values for the unknown parameters $\mu$ and $\sigma^2$ in the Gaussian by maximizing the likelihood function. In practice, it is more convenient to maximize the log of the likelihood function. Because the logarithm is monotonically increasing function of its argument, maximization of the log of a function is equivalent to maximization of the function itself. Taking the log not only simplifies the subsequent mathematical analysis, but it also helps numerically because the product of a large number of small probabilities can easily underflow the numerical precision of the computer, and this is resolved by computing instead the sum of the log probabilities.

can anyone give me some intuition behind it with some example? Where the log likelihood is more convenient over likelihood. Please give me a practical example.

Thanks in advance!