1 / 26

Warm-Up: February 1, 2012

Warm-Up: February 1, 2012. Simplify. Homework Questions?. Properties of Logarithms. Section 3.3. The Product Rule. Let b, M, and N be positive real numbers with b≠1 The logarithm of a product is the sum of the logarithms. Example 1. Expand and simplify. You-Try #1. Expand and simplify.

elma
Download Presentation

Warm-Up: February 1, 2012

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. Warm-Up: February 1, 2012 • Simplify

  2. Homework Questions?

  3. Properties of Logarithms Section 3.3

  4. The Product Rule • Let b, M, and N be positive real numbers with b≠1 • The logarithm of a product is the sum of the logarithms.

  5. Example 1 • Expand and simplify

  6. You-Try #1 • Expand and simplify

  7. The Quotient Rule • Let b, M, and N be positive real numbers with b≠1 • The logarithm of a quotient is the difference of the logarithms

  8. Example 2 • Expand and simplify

  9. You-Try #2 • Expand and simplify

  10. The Power Rule • Let b and M be positive real numbers with b≠1, and let p be any real number • The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of that number

  11. Example 3 • Expand and simplify

  12. You-Try #3 • Expand and simplify

  13. Expanding Logarithmic Expressions • First rewrite radicals as exponents • Use power rule, product rule, and quotient rule to expand the logarithm • Repeat step 2 as many times as necessary until the expression is COMPLETELY expanded • Evaluate any log terms that result in integers (i.e., log6362)

  14. Example 4 • Expand the following expression. (The word “completely” is always implied.)

  15. You-Try #4 • Expand each expression (the word “completely” is always implied)

  16. Warm-Up: Groundhog Day! Today is Groundhog Day! It is time for the annual Groundhog Day photo of Punxsutawney Phil with some of the members of his Inner Circle.  Can you help the members find their spots in the photo?  Read the clues below to place the Inner Circle members in their correct spots.   CLUES:1.  Big Chill is just to the right of Phil.2.  Stump Warden is not next to Thunder Conductor.3.  Rainmaker is not next to Thunder Conductor.4.  Rainmaker is not next to Big Chill.5.  Stump Warden is not next to Big Chill.6.  Thunder Conductor is not next to Phil.7.  Rainmaker is not next to Phil.

  17. Homework Questions?

  18. Condensing Logarithmic Functions • The sum and difference of logs can be combined into a single log iff they have the SAME BASE. • Use the power rule to move numbers being multiplied by log terms to exponents • Combine log terms using the product and quotient rules: If the term is positive, it goes on top, if it’s negative, it goes on bottom

  19. Example 5 • Write as a single logarithm

  20. You-Try #5 • Write as a single logarithm

  21. Change of Base • For logarithmic bases a and b, and positive number M • General log: • Common log: • Natural log:

  22. Example 7 • Use common log or natural log and your TI-83 to evaluate. Round to two decimal places.

  23. You-Try #7 • Use common log or natural log and your TI-83 to evaluate. Round to two decimal places.

  24. Assignment • Page 387 #1-77 Every Other Odd

More Related