It will first be relevant to summarise the rules of logarithms:

(1)

(2)

(3)

(4)

(5)

Often we can simplify a logarithmic expression so that it becomes either a single log, or a constant plus a log.

Example: Simplify

using (1)

using (3)

using (5)

Example: Ifexpressterms of p

using (1)

using (3)

Simplify

using (2)

using (5)

Simplify

from (2)