I know that the maximum possible Shannon Entropy for an alphabet $X$ is $\log|X|$, where Shannon Entropy is:
$$H(X) = - \sum_{x \in X} \; p(x) \log p(x)$$
but how is this upper limit computed?
I know that the maximum possible Shannon Entropy for an alphabet $X$ is $\log|X|$, where Shannon Entropy is:
$$H(X) = - \sum_{x \in X} \; p(x) \log p(x)$$
but how is this upper limit computed?