1 / 10

Logarithms

Logarithms. Objective: Students will use properties of logarithms to simplify expressions. Logarithmic Functions. Logarithmic Equation. y = log a x. exponent. /logarithm. x = 2 y is an exponential equation . If we solve for y it is called a logarithmic equation .

ganit
Download Presentation

Logarithms

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. Logarithms Objective: Students will use properties of logarithms to simplify expressions.

  2. Logarithmic Functions Logarithmic Equation y = loga x exponent /logarithm x = 2yis anexponentialequation. If we solve for y it is called alogarithmic equation. Let’s look at the parts of each type of equation: Exponential Equationx = ay base number In General, a logarithm is the exponent to which the base must be Raised to get the number that you are taking the logarithm of.

  3. base number exponent Example1 : Rewrite in exponential form a) solve loga64 = 2 a2 = 64 a = 8 b) Solve log5 x = 3 Rewrite in exponential form: 53 = x x = 125

  4. c) Solve An equation in the form y = logb x where b > 0 and b ≠ 1 is called a logarithmic function. 7y = 1 = 7-2 49 y = –2 Logarithmic and exponential functions are inverses of each other logb bx = x blogb x = x

  5. Examples 2 Evaluate each:a. log8 84b. 6[log6 (3y – 1)] logb bx = x log8 84= 4 blogb x = x 6[log6 (3y – 1)]=3y – 1 Here are some special logarithm values: 1. loga 1 = 0 because a0 = 1 2. loga a = 1 because a1 = a 3. loga ax = x because ax = ax

  6. Logarithms Consider 72 = 49. The logarithm of 49 to the base 7 is equal to 2 (log749 = 2). Logarithmic form Exponential notation log749 = 2 72 = 49 In general: Ifbx = N, then logbN = x. Ex 3 State in logarithmic form or State in exponential form: a) 63 = 216 log6216 = 3 c) log5125 = 3 53 = 125 d) log2128= 7 27 = 128 log416 = 2 b) 42 = 16

  7. Practice Evaluating Logarithms 1. log2128 2. log327 Note: log2128 = log227 = 7 log327 = log333 = 3 log327 = x 3x = 27 3x = 33 x = 3 log2128 = x 2x = 128 2x = 27 x = 7 3. log556 logaam = m = 6 4. log816 5. log81 log816 = x 8x = 16 23x = 24 3x = 4 log81 = x 8x = 1 8x = 80 x = 0 loga1 = 0

  8. Evaluating Logarithms 6. 7. log4(log338) = x log48 = x 4x = 8 22x = 23 2x = 3 2x = 1 8. = 23 = 8

  9. Evaluating Base 10 Logs Base 10 logarithms are called common logs. EX 4 Using your calculator, evaluate to 3 decimal places: a) log1025 b) log100.32 c) log102 1.398 -0.495 0.301 Common logs may also be written without the base 10 log 25 log 0.32 1og 2 d) ln 15 e) ln 0.12 f) ln 2 .693 -2.120 2.708

  10. Classwork P. 499 guided practice #1-13 Homework page 504 #9-27 odd

More Related