Ratios, Logarithms, and Decibels: Laws of logarithms (things to remember)

This post provides the laws of logarithms that may be frequently used to solve problems involving logarithms.

Law 1: log (m*n) = log (m) + log (n)

Example:
log (2*3) = log (2) + log (3);
log (2*3) = 0.3010 + 0.4771;
log (2*3) = 0.7781;

Law 2: log (m/n) = log (m) - log (n)

Example:
log (5/3) = log (5) - log (3);
log (5/3) = 0.6989 - 0.4771;
log (5/3) = 0.2218;

Law 3: log m^n = n * log (m)

Example:
log (5^2) = 2 * log (5);
log (5^2) = 2 * 0.6989;
log (5^2) = 1.3978;

Law 4: log (1/m) = - log (m)

Example:
log (1/2) = - log (2);
log (1/2) = - 0.3010;