Vocabulary
Base- The number or expression that is used as a factor in a repeated multiplication
Essential Information
Properties of Logarithms
Let b, m, and n be positive numbers such that b≠1.
Product Property logᵦmn = logᵦm=logᵦn
Quotient Property logᵦ(m/n) = logᵦm - logᵦn
Power Property logᵦmⁿ = nlogᵦm
Let b, m, and n be positive numbers such that b≠1.
Product Property logᵦmn = logᵦm=logᵦn
Quotient Property logᵦ(m/n) = logᵦm - logᵦn
Power Property logᵦmⁿ = nlogᵦm
Rewriting Expressions
You can use the properties of logarithms to expand and condense logarithmic expressions
You can use the properties of logarithms to expand and condense logarithmic expressions
Change of Base Formula
Logarithms with any base other than 10 or e can be written in the terms of common or natural logarithms using the change-of-base formula. Thisallows you to evaluate any logarithm using a calculator.
If a, b, and c, are positive numbers with b≠1 and c≠1, then:
Logarithms with any base other than 10 or e can be written in the terms of common or natural logarithms using the change-of-base formula. Thisallows you to evaluate any logarithm using a calculator.
If a, b, and c, are positive numbers with b≠1 and c≠1, then: