1. Lesson 6

1.4. Explore 3

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

In Try This 3 you may have noticed that logarithms can be used to solve exponential equations. Logarithms are especially helpful where the exponential equations contain bases that are not powers of one another and a common base cannot be found.

 

Remember these important points when solving exponential equations:

  • Take the logarithm of each side of the equation and then use the property if A = B, then logc A = logc B, where c, A, B > 0 and c ≠ 1.
  • The base of the logarithm used is often base 10, but any base can be used as long as the bases on each side of the equation are the same.
  • Once the logarithm has been applied, the laws of logarithms can be used to simplify the equation and solve for the variable.

There are two methods that can be used for some equations. One method is to take the logarithm of each side of the equation. The other method that may be used is to convert the exponential equation to logarithmic form. This second method works when there is a variable as an exponent on only one side of the equation.


textbook

Read “Example 2” on pages 408 to 409 of the textbook. Notice the following points when reading:

  • There are two methods that could be used in part a of the example. Only one method is shown for parts b and c.
  • Each value was checked to verify that the solution is correct.
  • The answers were rounded to two decimal places. The answer above the approximate solution is considered the exact value of the solution.
Self-Check 2

 

textbook

  1. Complete “Your Turn” at the end of “Example 2” on page 409 of the textbook. Answer
  2. Complete the matching activity Solving Exponential Equations Using Logarithms.

     
    This is a play button that opens Solving Exponential Equations Using Logarithms.