Lesson 6: Logarithmic and Exponential Equations

Focus

Do you have a savings account, RESP, or other type of investment? Do you enjoy watching your money grow and gain interest? If you have a car loan, credit card, or other borrowed money, you might have experienced interest in a different way! Whether you are calculating your interest on investments or your interest charges on loans, you will be using formulas that contain exponents.

In Lesson 2 you solved exponential equations in which the bases of the powers were the same and the exponents could be equated. When a common base of the powers could not be found, the equations were much more difficult to solve. How can you solve any exponential equation algebraically?

In this lesson you will explore how to solve equations that include logarithms and how logarithms will help solve exponential equations.

Lesson Outcomes

At the end of this lesson you will be able to

• solve logarithmic equations and verify the solution
• solve exponential equations when the bases are not powers of one another
• solve a problem by modelling a situation with an exponential or logarithmic equation

Lesson Question

You will investigate the following question:

• How can logarithmic or exponential equations be solved?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 6 Assignment (Download the Lesson 6 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection