Math 092 Module 5 Lesson 3 - Logarithmic Functions

This is Math 092 Module 5 Lesson 3. It introduces the notion of a logarithm as an inverse function to an exponential function. The focus in this lesson is to understand what a logarithm is, how it may be evaluated, and how logarithmic functions can be graphed as inverses of exponential functions with transformations. Further details about logarithm properties, simplifying logarithmic expressions, and solving equations with logarithms can be found in the subsequent videos. See the timestamps below to refer to specific parts of this lesson.

00:00 Logarithms overview
00:23 Opening scenario of an exponential situation that motivates the need for logarithms
4:05 Logarithm as an inverse operation to an exponential
4:45 Logarithm definition with examples of some simple cases
7:06 Converting between exponential form and logarithmic form with examples
13:53 Change of base formula (helps to use a calculator to evaluate a logarithm) with an example
15:22 Inverse properties of logarithms as used to simplify certain logarithms
17:24 Zero and one exponent properties as translated into logarithm properties
18:04 Graphing logarithmic functions as inverses of exponential functions