1 / 9

15.2 Logarithmic Functions

15.2 Logarithmic Functions. OBJ:  To find the base-b logarithm of a positive number  To find a base-b logarithm equation. P 394  If y = 2 x what is y – 1 ? x = 2 y log 2 x = log 2 2 y log 2 x = y – 1 y = log 2 x DEF:  Inverse of an exponential function

kiara
Download Presentation

15.2 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. 15.2 Logarithmic Functions OBJ:  To find the base-b logarithm of a positive number  To find a base-b logarithm equation

  2. P 394 If y = 2 x what is y – 1 ? x = 2 y log2x = log 22 y log2x = y – 1 y = log2x DEF:  Inverse of an exponential function y = logbx NOTE: Since y = 3 x and y = log 3 x are inverse functions, they are symmetric with respect to y = x and the graph of y = 3 x could be reflected in y = x to obtain y = log 3 x

  3. EX:  log 3 9 log 3 9 = x 3 x = 9 3 x = 3 2 x = 2 log 3 81 log 3 81= x 3 x = 81 3 x = 3 4 x = 4  log 3 1 log 3 1 = x 3 x = 1 3 x = 3 0 x = 0  log 3 1/3 log 3 1/3 = x 3 x = 1/3 3 x = 3 -1 x = - 1 DEF: Base – b logarithmIf y = b x , then log b y = x

  4. log 3 3 log 3 3 = x 3 x = 3 ½ x = ½ log 3 1/27 log 3 1/27 = x 3 x = 3-3 x = -3 EX: 1 log 10 100 P 392 log 10 100 = x 10 x = 102 x = 2 log 2 1/16 log 2 1/16 = x 2 x = 2- 4 x = - 4 EX 2  log 34 3 P 392 log 34 3 = x 3 x = 3 ¼ x = 1/4  log 25 8 log 25 8 = x 2x = (23)1/5 x = 3/5

  5. EX: 3 log b 81 = 4 P393b 4 = 81 b 4 = 3 4 b = 3 log 5 625 = x 5 x = 625 5 x = 5 4 x = 4 log 4 y = 3 4 3 = y y = 64 log b1/8 = - 3 b -3 = 1/8 b -3 = 2 -3 b = 2 Solve each logarithmic equation for the variable.HW4 P393 (1-28 all)

  6. EX:  a = log b c; t = b v b a = c; v = log b t 4 = log 2 16 2 4 = 16 9/16 = (3/4)2 2 = log ¾ 9/16  5 = log b 70 b5 = 70  60 = 4 q q = log 4 60 Rewrite the logarithmic equations in exponential form and the reverse procedure.

  7. EX:  log 5 625 log 5 625 = x 5 x = 625 5 x = 5 4 x = 4  log 7 1 log 7 1 = x 7 x = 1 7 x = 7 0 x = 0  log 7 7 log 7 7 = x 7 x = 7 7 x = 7 1 x = 1 log 5 5 log 5 5 = x 5 x = 5 ½ x = ½ Find each logarithm.

  8. EX:  log 35 81 log 35 81 = x 3x = 5 81 3x = 34/5 x = 4/5 log 1/3 1/9 log 1/3 1/9 = x (1/3)x = 1/9 (1/3)x = (1/3)2 x = 2 log 1/3 9 log 1/3 9 = x (1/3)x = 9 3-x = 32 x = -2 EX:  log b 10,000 = 4 b4 = 10,000 b4 = 104 b = 10  log 3 y = 5 35 = y 243 = y EX:  1/81 = b– 4 3– 4 = b– 4 3 = b 1/8 = b – 3 (2)– 3= b– 3 2 = b Find each logarithm. Solve each equation.

  9. 9 = r – 2/3 32 = r – 2/3 (32)-3/2 = (r – 2/3)-3/2 3 -3 = r 1/27 = r z 5/2 = 243 z 5/2 = 3 5 (z5/2)2/5= (3 5)2/5 z = 32 z = 9 Solve. HW 3 (35-38)

More Related