Math
Logarithm properties.
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
Real-world.
- 1 log(2 × 3) = log 2 + log 3 (product rule)
- 2 log(8/4) = log 8 − log 4 (quotient rule)
- 3 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