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In Discover you rearranged exponential expressions to have the same base. For example, you may have found the following equivalent expression:
By rewriting all three expressions as base 2, you can see the expressions are all identical.
In Try This 1 you were changing the base of the powers so they were all base 2. In this lesson you will be changing powers to a different base. To do this you will have to use your knowledge of powers. For example, 64 can be written as base 2, base 4, or base 8.
64 = 26
64 = 43
64 = 82
If you are unsure of the exponent, you can check using your calculator.
To see an example of how to change the base of powers, read “Example 1” on page 360 of the textbook. Notice how laws of powers are used to simplify each expression.
Rewriting expressions with a common base allows you to compare the expressions and find equivalent expressions. It is very difficult to compare exponential expressions if they do not have the same base. Keep this important idea in mind as you complete Try This 2.
Try This 2
- Solve the equation 2x = 8 algebraically for x. Describe how you determined the value of x.
- Apply the method you used in question 1 to solve the following equations. For each equation, describe how you solved for the value of x.
- Solve for x in the equation 2x − 1 = 8.
- Solve for x in the equation 2x = 8x − 1.
Save your responses in your course folder.
Share 2
With a partner or group, discuss the following question based on your solutions in Try This 2:
Describe the methods you used to solve for x. Did you use the same method for each question? Why or why not? Do you need a more efficient method to solve these questions?
If required, save a record of your discussion in your course folder.
Would the algebraic method of changing the bases of each power to be the same base help solve for x?
8 can be written as a power with base 2.
