1 / 31

College Algebra Chapter 4 Exponential and Logarithmic Functions

Explore and apply Product, Quotient, and Power Properties as well as examples of expanding, simplifying logarithmic expressions. Practice Change-of-Base Formula along with sum, difference transformations. Utilize calculator for precise approximations.

schroeter
Download Presentation

College Algebra Chapter 4 Exponential and Logarithmic Functions

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. College AlgebraChapter 4Exponential and Logarithmic Functions Section 4.4 Properties of Logarithms

  2. 1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

  3. Apply the Product, Quotient, and Power Properties of Logarithms Let b, x, and y be positive real numbers where b ≠ 1. Product Property: Quotient Property: Power Property: For these exercises, assume that all variable expressions represent positive real numbers.

  4. Examples 1 – 3: Use the product property of logarithms to write the logarithm as a sum. Then simplify if possible. 1. 2. 3.

  5. Examples 4 – 6: Use the quotient property of logarithms to write the logarithm as a difference. Then simplify if possible. 4. 5. 6.

  6. Examples 7 – 9: Apply the power property of logarithms. 7. 8. 9.

  7. 1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

  8. Example 10: Write the expression as the sum or difference of logarithms.

  9. Example 11: Write the expression as the sum or difference of logarithms.

  10. Example 12: Write the expression as the sum or difference of logarithms.

  11. Example 13: Write the expression as the sum or difference of logarithms.

  12. Example 14: Write the expression as the sum or difference of logarithms.

  13. Example 15: Write the expression as the sum or difference of logarithms.

  14. 1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

  15. Example 16: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

  16. Example 17: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

  17. Example 18: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

  18. Example 19: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

  19. Example 20: Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

  20. Examples 21 – 23: Use to approximate the value of 21. 22. 23.

  21. 1. Apply the Product, Quotient, and Power Properties of Logarithms 2. Write a Logarithmic Expression in Expanded Form 3. Write a Logarithmic Expression as a Single Logarithm 4. Apply the Change-of-Base Formula

  22. Apply the Change-of-Base Formula Let a and b be positive real numbers such that a ≠ 1 and b ≠ 1. Then for any positive real number x In particular,

  23. Examples 24, 25: Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. 24. 25.

More Related