Logarithms and their Properties plus Practice
Logarithms AND their Properties Definition of a logarithm: If and is a constant , then if and only if . In the equation is referred to as the logarithm, is the base, and is the argument. The notation is read the logarithm (or log) base of . The definition of a logarithm indicates that a logarithm is an exponent. is the logarithmic form of is the exponential form of Examples of changes between logarithmic and exponential forms: Write each equation in its exponential form. a. b. c. Solution: Use the definition if and only if . a. b. a ! " # . c. a ! " % . Write the following in its logarithmic form: &' Solution: Use a ! " . Equality of Exponents Theorem: If is positive real number such that % , then . Example of Evaluating a Logarithmic Equation: Evaluate: & Solution: & a !
LOGARITHMS AND THEIR PROPERTIES Definition of a logarithm: If and is a constant , then if and only if . In the equation is referred to as the logarithm, is the base , and is the argument.
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