html5-img
1 / 30

7-4

7-4. Properties of Logarithms. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 2. Holt Algebra 2. Opener-NEW SHEET-12/9. Simplify. 1. (2 6 )(2 8 ). 2 14. 3 3. 2. (3 –2 )(3 5 ). 4 4. 3 8. 3. 4. 7 15. 5. (7 3 ) 5. Write in exponential form. 6. log x x = 1.

capricorn-rosas
Télécharger la présentation

7-4

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. 7-4 Properties of Logarithms Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2 Holt Algebra 2

  2. Opener-NEW SHEET-12/9 Simplify. 1. (26)(28) 214 33 2. (3–2)(35) 44 38 3. 4. 715 5. (73)5 Write in exponential form. 6. logxx = 1 7. 0 = logx1 x1 = x x0 = 1

  3. 2 3 2. Change log279 = to exponential form. 7-3 Hmwk Quiz 1. Change 64 = 1296 to logarithmic form. Calculate the following using mental math. 3. log 10,000 4. log264

  4. Objectives Use properties to simplify logarithmic expressions. Translate between logarithms in any base.

  5. The logarithmic function for pH that you saw in the previous lessons, pH =–log[H+], can also be expressed in exponential form, as 10–pH= [H+]. Because logarithms are exponents, you can derive the properties of logarithms from the properties of exponents

  6. 7-4 Explore

  7. 1 1 3 3 1 log27 + log 9 Example 1: Adding Logarithms Express log64 + log69 as a single logarithm. Simplify. log5625 + log525

  8. Example 2: Subtracting Logarithms Express log5100 – log54 as a single logarithm. Simplify, if possible. Express log749 – log77 as a single logarithm. Simplify, if possible.

  9. 1 2 Check It Out! Example 3 Express as a product. Simplify, if possibly. a. log104 b. log5252 c. log2 ( )5

  10. Jigsaw

  11. Example 4: Recognizing Inverses Simplify each expression. c. 5log510 a. log3311 b. log381 log3311 log33  3  3 3 5log510 log334 10 11 4

  12. Check It Out! Example 5a Continued Evaluate log816. Evaluate log927.

  13. Remember that to multiply powers with the same base, you add exponents.

  14. The property in the previous slide can be used in reverse to write a sum of logarithms (exponents) as a single logarithm, which can often be simplified. Helpful Hint Think: logj+ loga+ logm = logjam

  15. Remember that to divide powers with the same base, you subtract exponents Because logarithms are exponents, subtracting logarithms with the same base is the same as finding the logarithms of the quotient with that base.

  16. Caution Just as a5b3 cannot be simplified, logarithms must have the same base to be simplified. The property above can also be used in reverse.

  17. Because you can multiply logarithms, you can also take powers of logarithms.

  18. Example 3: Simplifying Logarithms with Exponents Express as a product. Simplify, if possible. B. log8420

  19. Exponential and logarithmic operations undo each other since they are inverse operations.

  20. Check It Out! Example 4 a. Simplify log100.9

  21. Most calculators calculate logarithms only in base 10 or base e (see Lesson 7-6). You can change a logarithm in one base to a logarithm in another base with the following formula.

  22. Example 5 Continued Evaluate log328.

  23. Opener-Same sheet-12/12 2. Simplify 2log2(8x) 1. log5625 + log525 3. log2326 4. Evaluate log927.

  24. 7 6 Team Problems Express each as a single logarithm. 1. log69 + log624 log6216 = 3 log327 = 3 2. log3108 – log34 Simplify. 3. log2810,000 30,000 4. log44x –1 x – 1 5. 10log125 125 6. log64128

  25. Signs

  26. Pick any of the two properties and describe how to solve them and give an example of how to do them. Type 2

  27. 8. log 10 1 2 Lesson Quiz: Part II Use a calculator to find each logarithm to the nearest thousandth. 2.727 7. log320 –3.322 9. How many times as much energy is released by a magnitude-8.5 earthquake as a magntitude-6.5 earthquake? 1000

More Related