I know some basic laws of logs, such as $$c \cdot \log(x) = \log(x^c)$$ $$\log(xy) = \log(x) + \log(y)$$ $$\log(\frac{x}{y}) = \log(x) - \log(y)$$
But I just can't see how $$\frac{1}{2} \cdot (1 - p^2-q^2) \cdot \log_2(1-p^2-q^2)$$ turns into $$pq \cdot \log_2(2pq)$$
EDIT: This is from a probability paper on coin flipping, so that $q = 1-p$.
$$p+q=1 \implies (p+q)^2=1 \implies p^2+q^2+2pq=1 \implies 1-p^2-q^2=2pq$$ Thus $$\frac{1}{2} \cdot (1 - p^2-q^2) \cdot \log_2(1-p^2-q^2)=pq\log_{2}(2pq)$$