5-6-solving-exponential-and-logarithmic-equations - Objectives 1 Solve exponential and logarithmic equations 2 Solve a variety of application problems

5-6-solving-exponential-and-logarithmic-equations -...

This preview shows page 1 - 9 out of 27 pages.

Objectives: 1. Solve exponential and logarithmic equations. 2. Solve a variety of application problems by using exponential and logarithmic equations. Solving Exponential and Logarithmic Equations 5.6
Image of page 1
Methods of Solving Exponential Equations 1.Rewrite the bases of the powers on both sides so they are the same. . .
Image of page 2
Example #1 Powers of the Same Base Solve the equation and confirm your solution with a graph. A. 1 3 9 x x Rewrite both bases to base 3. 1 1 2 3 3 3 3 1 2 1 2 x x x x x x x
Image of page 3
Example #1 Powers of the Same Base Solve the equation and confirm your solution with a graph. B. 5 3 4 1 2 x x Rewrite to base 2, remember fractions have negative exponents. 10 2 3 5 2 3 5 1 2 3 5 1 3 2 2 2 2 2 2 4 2 x x x x x x x x 3 13 13 3 10 3 3 10 2 3 x x x x x
Image of page 4
Example #1 continued… Powers of the Same Base Solve the equation and confirm your solution with a graph. C. 625 25 5 2 x x Rewrite to base 5. 1 4 4 5 5 5 5 5 5 5 5 5 5 4 4 4 2 2 4 2 2 4 2 2 x x x x x x x x x
Image of page 5
Example #1 continued… Powers of the Same Base Solve the equation and confirm your solution with a graph. D. x x 32 2 6 2  1 , 6 0 1 6 0 6 5 5 6 2 2 2 2 2 2 5 6 5 6 2 2 x x x x x x x x x x x x This time the graphs with the intersection method were too difficult to read, so the intercept method was used to verify the two solutions.
Image of page 6
Example #2 Logarithms on Both Sides Solve the equation. Solutions can be confirmed with a graph. 3 6 x Problems like this can be confusing because students will recognize that 2(3) = 6. Unfortunately, that will not work because we have to be able to rewrite both sides to the same base of a power for the first method to be used. Our only choice then is the second method. 6131 . 0 6 log 3 log 3 log 6 log 3 log 6 log x x x 6131 . 0 6 ln 3 ln 3 ln 6 ln 3 ln 6 ln x x x Notice how common logs and natural logs both work the same way. Choosing which one to use basically comes down to personal preference.
Image of page 7
Image of page 8
Image of page 9

You've reached the end of your free preview.

Want to read all 27 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture