First, as others have mentioned, we usually work with the logarithm of the likelihood function, for various mathematical and computational reasons.
Second, since the likelihood function depends on the data, it is convenient to transform it to a function with standardized maxima (see Pickles 1986).$$R(\theta) = \frac{L(\theta)}{L(\theta^\ast)} \quad \text{where } \theta^\ast = \arg \max_{\theta} L(\theta)$$
set.seed(123)random_numbers <- rnorm(50, mean = 5, sd = 5)max_likelihood <- prod(dnorm(random_numbers, mean = 5, sd = 5))nonmax_likelihood <- rep(0,1000)j <- 1 for (k in seq(0,10,length.out=1000)) { nonmax_likelihood[j] <- prod(dnorm(random_numbers, mean=k, sd=5)) j <- j+1}par(mfrow = c(1, 2))plot(seq(0,10,length.out=1000),nonmax_likelihood/max_likelihood, xlab="Mean", ylab="Relative likelihood")plot(seq(0,10,length.out=1000),log(nonmax_likelihood) - log(max_likelihood), xlab="Mean", ylab="Relative log-likelihood")