Logarithm properties

Math

Definition

Rules that simplify expressions involving logarithms. The three main properties are the product rule, quotient rule, and power rule, which convert between multiplication, division, and exponents inside logarithms.

Examples

  • log(2 × 3) = log 2 + log 3 (product rule)
  • log(8/4) = log 8 − log 4 (quotient rule)
  • log(2³) = 3·log 2 (power rule)
Key Fact

Product: log(ab) = log a + log b; Quotient: log(a/b) = log a − log b; Power: log(aⁿ) = n·log a

Related Terms

Logarithmic properties Natural log Solving log equations Exponent rules

Study This Concept

Practice logarithm properties with free review games in these units:

Algebra 2 Unit 7: Exponential and Logarithmic Functions