Properties of Logarithms

Explanation

Logarithms have rules that simplify calculations:

1. Product rule: logₐ(M·N) = logₐ(M) + logₐ(N)

2. Quotient rule: logₐ(M/N) = logₐ(M) − logₐ(N)

3. Power rule: logₐ(Mᵖ) = p·logₐ(M)

4. Change of base formula: logₐ(M) = logᵦ(M) / logᵦ(a)

Example:
log₂(8·4) = log₂(8) + log₂(4) = 3 + 2 = 5