Change of base rule
\(\log_a b = \dfrac{\log_c b}{\log_c a}\)

Power rule
\(\log_b(M^p) = p\log_b(M)\)

Proof of the logarithm quotient and power rules

Product rule
\(\log_b(MN) = \log_b(M) + \log_b(N)\)

Proof of the logarithm product rule

Quotient rule
\(\log_b\left(\dfrac{M}{N}\right) = \log_b(M) - \log_b(N)\)

Proof of the logarithm quotient and power rules