Section 3.2 Logarithmic Functions 1 Section 3.2 Logarithmic Functions (Complete problems in purple before class) Definition: Logarithmic Function For a > 0 and a ? 1, the logarithmic function with base a denoted f ( x) = log a ( x), where ? = log?(?) if and only if ? ? = ? Note that log a( 1) = 0 for any base a, because a 0 = 1 for any base a. ? There are two bases that are used more frequently than others; they are 10 and e. ? The notation log 10( x) is abbreviated log( x) and log e( x) is abbreviated ln( x), which are called common logarithms and natural logarithms, respectively. Note: log x means x10log : base 10 ln e means xelog : base e One-to-One Property of Logarithms