1 / 16

Solve exponential and logarithmic equations and equalities.

Objectives. Solve exponential and logarithmic equations and equalities. Solve problems involving exponential and logarithmic equations. Vocabulary. exponential equation logarithmic equation.

regane
Download Presentation

Solve exponential and logarithmic equations and equalities.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Objectives Solve exponential and logarithmic equations and equalities. Solve problems involving exponential and logarithmic equations.

  2. Vocabulary exponential equation logarithmic equation

  3. An exponential equation is an equation containing one or more expressions that have a variable as an exponent. To solve exponential equations: • Try writing them so that the bases are all the same. • Take the logarithm of both sides.

  4. Helpful Hint When you use a rounded number in a check, the result will not be exact, but it should be reasonable.

  5. Check It Out! Example 1a Solve and check. 32x = 27

  6. Check It Out! Example 1b Solve and check. 7–x = 21

  7. Check It Out! Example 1c Solve and check. 23x = 15

  8. Check It Out! Example 2 You receive one penny on the first day, and then triple that (3 cents) on the second day, and so on for a month. On what day would you receive a least a million dollars.

  9. A logarithmic equation is an equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms.

  10. Remember! Review the properties of logarithms from Lesson 7-4.

  11. Check It Out! Example 3a Solve. 3 = log 8 + 3log x

  12. Check It Out! Example 3b Solve. 2log x– log 4 = 0

  13. Caution Watch out for calculated solutions that are not solutions of the original equation.

  14. Check It Out! Example 4a Use a table and graph to solve 2x = 4x – 1. Use a graphing calculator. Enter 2xas Y1 and4(x – 1)as Y2. In the graph, find the x-value at the point of intersection. In the table, find the x-values where Y1 is equal to Y2. The solution is x = 2.

  15. Check It Out! Example 4b Use a table and graph to solve 2x > 4x – 1. Use a graphing calculator. Enter 2xas Y1 and4(x – 1)as Y2. In the graph, find the x-value at the point of intersection. In the table, find the x-values where Y1 is greater than Y2. The solution is x < 2.

  16. Check It Out! Example 4c Use a table and graph to solve log x2 = 6. Use a graphing calculator. Enter log(x2)as Y1 and6 as Y2. In the graph, find the x-value at the point of intersection. In the table, find the x-values where Y1 is equal to Y2. The solution is x = 1000.

More Related