Math 092 Module 5 Lesson 5 - Exponential and Logarithmic Equations and Applications

This is Math 092 Module 5 Lesson 5. It includes a recap of what we know about logarithms in this module so far and introduces strategies for solving exponential and logarithmic equations. It also shows some contexts in which these strategies can be useful. See the timestamps below to refer to specific parts of this lesson.

0:00 Summary of what we know about logarithms - change of base, graphing, etc. towards how it will help us solve equations that involve logarithms
3:40 Summary of logarithm properties from previous lesson that will help in solving equations
5:45 Solving equations introduction
8:32 Example 1 - Solving an exponential equation with a logarithm
11:00 Example 2 - Solving a logarithmic equation with an exponential
12:02 Example 3 - Solving an exponential equation with different bases (challenging)
13:44 Example 4 - Solving a logarithmic equation that requires simplifying with logarithm laws first
14:25 Reminder to always check domain in equations involving logarithms
18:13 Example 5 - Solving a logarithmic equation that reduces to a factorable quadratic equation
19:18 Example 6 - Solving a logarithmic equation that requires simplifying first and results in a non-factorable quadratic equation
22:31 Short summary of approaches for solving equations with logarithms
23:24 Example 7 - Solving an exponential equation
27:06 Examples 8 & 9 - Two more practice examples for solving exponential equations, with the second one done in a few ways
31:25 Example 10 - Solving another example of an exponential equation with different bases with the use of ln
34:23 Examples of application examples for logarithms in contexts of exponential growth and decay