Module 6: Exponents and Logarithms

 

Your work from Try This 3 might have looked something like this:

 

42x = 83x−2

 

(22)2x = (23)3x−2

Change 4 and 8 to a powers with base 2.

Apply the power of a power exponent law and multiply the exponents together. Don’t forget to use the distributive property when multiplying a binomial.

There is a single power on each side of the equation. The exponents are equal.
LS RS

Left Side = Right Side

 



The solution is

Verify. You could substitute the value for x into the original equation to check your solution.
This is a graph of two exponential functions. One function is y equals 4 to the exponent 2 times x. The second function is y equals 8 to the exponent 3 times x subtract 2. The intersection point of the two curves is labelled at 1.2, 27.86.

You could use a graphical method to determine the value of x.

 

The x-value of the intersection point is 1.2, so the solution is x = 1.2, or .
This is a photo of a man in a wheechair using a calculator.
Jupiterimages/Comstock/Thinkstock

You may remember from Lesson 1 that radioactive material decay is measured in half-life. Half-life is the amount of time it takes for half of a radioactive material to decay. In the example Solving an Exponential Equation, the half-life of Sodium-24 is used to find out how long it will take for the material decay to  of its original mass. In order to find the solution, powers will be changed to the same bases. Notice how there are two choices as to what base can be used.

 

This is a play button that opens Solving an Exponential Equation.

 

tip

When entering powers into your calculator, use brackets around the exponent. For example, to enter 32x−3 into your calculator, type 3, ^(this is the exponent button), bracket, 2x − 3, bracket.



Self-Check 2

 

textbook

  1. Complete “Your Turn” part b at the end of “Example 2” on page 361 of the textbook. Answer
  2. Complete question 9 on page 364 of the textbook. Answer
  3. Complete question C2 on page 365 of the textbook. Answer

In Try This 3 you solved an exponential equation where the base of each power could be expressed with a common base. How would you solve an equation where a common base could not be found?

 

Try This 4
  1. The exponential equation 3x = 4 cannot be solved using the method used in Try This 3. Why is this?
  2. Try different strategies to solve the equation. Verify the solution of each strategy by substitution.

course folder Save your responses in your course folder.