Expert: Scott A Wilson - 4/14/2011

Question
Express the logarithm in terms of log2M and log2N:

log2(MN)4

Answer
It is known that [1] log(ab) = log(a) + log(b) and [2] log(a^n) = n*ln(a).

This mean that if we are talking about logs base 2, as I read log2M and log2N to be,
we'll just refer to it as log to keep things simpler.  I'll also assume that log(MN)4
is log[(MN^4)].

This makes the question be to express log^4(MN) in terms of log(M) and log(N).

Using gproperty [2], log[(MN)^4] can be rewritten as 4*log(MN).
Using property [1], if we look at log(MN), that can be rewritten as log(M) + log(N).
Since we have log(MN) times 4, that can be rewritten as 4*(log(M) + log(N)) or
4*log(M) + 4*log(N).