Mathematics - Functions - Logarithmic - Properties of logarithms - Three Log Properties

9 steps: (1) PRODUCT RULE: log_b(MN) = log_b(M) + log_b(N). (2) Why? If b^p=M and b^q=N, then MN=b^(p+q), so log_b(MN)=p+q. (3) Example: log₂(8·4) = log₂(8) + log₂(4) = 3+2 = 5. Check: log₂(32) = 5 ✓. (4) QUOTIENT RULE: log_b(M/N) = log_b(M) - log_b(N). (5) Example: log₃(81/9) = log₃(81) - log₃(9) =