1 / 11

8.4 Logarithmic Functions 4/8/2013

8.4 Logarithmic Functions 4/8/2013. Definition of a Logarithmic Function. log b n = p is equivalent to b p = n (logarithmic form) (exponential form). Exponent. Exponent. Base. Base. Location of Base and Exponent in Exponential and Logarithmic Forms.

step
Download Presentation

8.4 Logarithmic Functions 4/8/2013

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. 8.4 Logarithmic Functions 4/8/2013

  2. Definition of a Logarithmic Function logbn = p is equivalent to bp=n (logarithmic form) (exponential form)

  3. Exponent Exponent Base Base Location of Base and Exponent in Exponential and Logarithmic Forms Logarithmic form:p= logbn Exponential Form: bp=n

  4. Base 10 log 10x = log x is called a common logarithm Base “e” log ex = lnx is called the natural logarithm Popular Bases have special names

  5. Example 1 24 16 = b. log7 1 0 70 1 = = c. log5 5 1 51 5 = = d. log0.01 2 0.01 = = – 10 2 – e. log1/4 4 1 4 = = – 1 1 – 4 Rewrite Logarithmic Equations logbn = p is bp= n EXPONENTIAL FORM LOGARITHMIC FORM a. log2 16 4 =

  6. Checkpoint 34 81 = ANSWER 2. log4 4 1 41 4 = = ANSWER 3. log6 1 0 60 1 = = ANSWER 4. log1/2 4 2 4 = = – ANSWER 2 1 – 2 Rewrite Logarithmic Equations logbn = p is bp= n Rewrite the equation in exponential form. 1. log3 81 4 =

  7. Basic Logarithmic Properties Involving One • Logbb = 1 because 1 is the exponent to which b must be raised to obtain b. (b1 = b). • Logb 1 = 0 because 0 is the exponent to which b must be raised to obtain 1. (b0 = 1).

  8. Example 2 SOLUTION To help you find the value of logbn, ask yourself what power of b gives you n. a. 4? 64 = What power of 4 gives 64? 43 64 = Guess, check, and revise. log4 64 3 = Evaluate Logarithmic Expressions logbn = p is bp= n Evaluate the expression. a. b. c. log4 64 log4 2 log1/3 9

  9. Example 2 1 41/2 2 = Guess, check, and revise. log4 2 = 2 ? 1 c. 9 = What power of gives 9? 3 1 3 2 1 – 9 = Guess, check, and revise. 3 log1/3 9 2 = – b. 4? 2 = What power of 4 gives 2? Evaluate Logarithmic Expressions

  10. Evaluate and Simplify Logarithmic Expressions Checkpoint 6 ANSWER . 6. Evaluate log4 ANSWER 1 2 ANSWER 1 16 2 – 5. Evaluate log2 64. 7. Evaluate log16 4.

  11. Homework: Prac A WS 8.4

More Related