The log of a number raised to a power is the power times the log of the number. $\log_b(a^n) = n \log_b(a)$ The log of two numbers multiplied is the sum of the log of each number. $\log_bM*N = \log_bM + \log_bN$ The log of a number divided by another number is the difference of the log of each number. $\log_b\frac{M}{N} = \log_bM - \log_bN$ The log of the base of the number is 1. $\log_b b = 1$ The log of the base of the same number to a power of $k$ is $k$. $\log_b b^k = k$ The log of $1$ is $0$. $\log_b 1 = 0$