How does changing the log base affect the intepretation of information entropy Entropy of random variable is defined as:
$$H(X)= \sum_{i=1}^n p_i \log_2(p_i)$$
Which as far as I understand can be interpreted as how many yes/no questions one would have to ask on average, to find out the value of the random variable $X$.
But what if the log base is changed to for example e? What would the interpretation be then? Is there an intuitive explanation?

One has
$$\log_a(x)=\frac{\log b}{\log a}\:\log_b(x)$$
thus
$$H(X)= \sum_{i=1}^n p_i \log_a(p_i)=\frac{\log b}{\log a}\sum_{i=1}^n p_i \log_b(p_i)$$ or
$$
H_a(X)=\frac{\log b}{\log a}H_b(X).
$$
