Module 6: Exponents and Logarithms

 

In Try This 2 you were working with exponential equations. 2x = 8x−1 is an exponential equation because the equation has a variable, x, in the exponent.

 

In Discover you may have changed the bases in an expression so they were the same on each side. This helped you compare and determine if the expressions were equal. You may have used a similar strategy to solve the exponential equations in Try This 2.

 

When the bases are the same on each side of an equation, the exponents on each side of the equation must be equal. This can be expressed by the property that if bx = by, then x = y and b ≠ −1, 0, 1.

 

For example, in Try This 2 you solved 2x = 8x−1.

 

 

 

To use this property to solve exponential equations, there must be only one power on each side of the equation and the bases of each power must be the same. At times, the exponent laws may need to be used to change the base of a power.



textbook

Read “Example 2” part a on page 360 of the textbook. Notice that two methods are shown. Method 1 solves the equation by changing bases, and Method 2 uses graphing to solve the equation. Solving exponential equations using a graphical method is valid, but the focus for this lesson is on using an algebraic approach to solve exponential equations.

 

Self-Check 1
  1. Complete “Your Turn” at the end of “Example 1” on page 360 of the textbook. Answer
  2. Complete “Your Turn” part a at the end of “Example 2” on page 361 of the textbook. Answer
  3. Complete question 4.c. on page 364 of the textbook. Answer
  4. Refer to the property, if bx = by, then x = y and b ≠ −1, 0, 1. Explain why there is a restriction that b ≠ −1, 0, 1. Answer