Question

Can somebody explain to me how to determine which of these statements are true (possibly more than one correct answer)?

A. logM - logN = log(M - N)
B. logM + logN = log(MN)
C. logM^p = p * logM
D. (logM)^p = p * logM

Answer 1

There are a few logarithmic identities.
If you know those identities you can quickly identify which of the choices are true.

log(M) - log(N) = log(M / N)
log(M) + log(N) = log(M * N)
log(M^p) = p * log(M)
(log(M))^p = log(M) * og(M) * og(M) * .... p times

Answer 2

(log(M))^p = log(M) * log(M) * log(M) * .... p times