Logarithmic Functions Let a be a positive number with a ≠ 1. The logarithmic function with base a, denoted by loga, is defined by is the exponent to which the base a must be raised to give x. Ex 1: Rewrite in exponential form a. b.

Ex 2: Rewrite in logarithmic form a. b. Ex 3: Evaluate a. b. c.

Properties of Logarithms We raise a to the 0 power to get 1. We raise a to the 1 power to get a. We raise a to the x power to get ax. loga x is the power to which a must be raised to get x.

Ex 4: Evaluate a. b. c. d.

Ex 5: Graph by graphing

Ex 6: Graph and

Ex 7: Find the domain of and sketch the function. D:

Ex 8: Find the domain of and sketch the function. D:

The logarithm with base 10 is called the common The logarithm with base 10 is called the common logarithm and is denoted by omitting the base: Ex 9: Use a calculator to evaluate. a. b.

Ex 10: The perception of loudness B (in decibels) Ex 10: The perception of loudness B (in decibels) of a sound with physical intensity I is given by where I0 is the physical intensity of a barely audible sound. Find the decibel level of a sound whose physical intensity I is 100 times that of I0.

Properties of Natural Logarithms The logarithm with base e is called the natural logarithm and is denoted by ln: Properties of Natural Logarithms We raise e to the 0 power to get 1. We raise e to the 1 power to get a. We raise e to the x power to get ex. ln x is the power to which e must be raised to get x.

Ex 12: Find the domain of the function Ex 11: Evaluate the following. a. b. c. Ex 12: Find the domain of the function D:

Assignment (#30) S 5.2: pg 406 - 407 #2,3,10,11,14,24,32,33,36, 39-43,58-60