Logarithmic properties

Math

Definition

The fundamental rules governing logarithmic expressions, including the product, quotient, and power rules, as well as the change of base formula. These properties are essential for solving logarithmic and exponential equations.

Examples

  • Using the power rule to bring down an exponent: ln(e³) = 3
  • Condensing log 5 + log 4 into log 20
  • Applying change of base: log₃(7) = ln 7 / ln 3
Key Fact

Change of base: logₐ(b) = log(b)/log(a) = ln(b)/ln(a)

Related Terms

Logarithm properties Natural log Solving log equations Solving exponential equations

Study This Concept

Practice logarithmic properties with free review games in these units:

Pre-Calculus Unit 3: Exponential and Logarithmic Functions