Download presentation

Presentation is loading. Please wait.

Published byKenia Bone Modified over 2 years ago

1
15.4 Logs of Products and Quotients OBJ: To expand the logarithm of a product or quotient To simplify a sum or difference of logarithms

2
What do you with the exponents when they are inside parenthesis? (x 3 )(x 4 ) You add them!! (Inside—Add) (x 3 )(x 4 ) x (3 + 4) x7x7

3
DEF: (1) Log b of a product log b (x · y) = log b x + log b y Inside parenthesis—Add logs

4
What do you with the exponents when they are in a quotient? x3x3 x4x4 You subtract them! (Quotient—Subtract) x3x3 x4x4 x (3 – 4)

5
DEF: (2) Log b of a quotient log b (x / y) = log b x – log b y Quotient—Subtract logs

6
HW 5 p399 ( 2, 4, 6, 24, 26) P397 EX: 1 Expand log 3 (5c/ d) How many log 3 do I need to write? log 3 log 3 log 3 log 3 ___ log 3 5 + log 3 c – log 3 – log 3 d

7
EX: Expand log b (7m/3n) log b 7 + log b m – log b 3 –log b n

8
HW 5 P 399 (10, 12,14, 28) P398EX:3Write as one logarithm: log 3 7 + log 3 t – log 3 4 – log 3 v log 3 (7t 4v)

9
EX: Write as one logarithm: log 2 9 + log 2 3c – log 2 c – log 2 5c log 2 (27c 5c 2 ) = log 2 (27 5c)

10
15.5 Logs of Powers and Radicals OBJ: To expand a logarithm of a power or a radical To simplify a multiple of a logarithm

11
What do you with the exponents when they are Outside parenthesis? (x 3 ) 4 You multiply them!! (Outside—multiply) (x 3 ) 4 x34x34 x 12

12
DEF: (3) Log b of a power Log b (x) r = r log b (x) Outside—Multiply (out in front of log)

13
HW 5 P402 ( 2, 4, 6, 26, 28) P 400 EX1: Expand log 5 (mn 3 ) 2 How many log 5 do I write in the parenthesis and with what symbol in between? (log 5 m + log 5 n) Where does the outside exponent of 2 and the inside exponent of 3 go? 2 (log 5 m + 3log 5 n)

14
P400 EX : 1 Expand log b 4 (m 3 / n) What does 4 (read as fourth root) become out in front of the parenthesis and what symbol is separating the terms in the parenthesis ? ( )( – ) (1/4)(3log b m – log b n)

15
HW5 P402 (10,12,14,32,34) P401EX:3 Write as one log: 5 log 2 c + 3 log 2 d log 2 (c 5 d 3 ) EX:4 1/3(log 5 t + 4 log 5 v – log 5 w) log 5 3 tv 4 /w

16
EX: Expand log 2 (5c 2 / d ) 3 3(log 2 5 + 2log 2 c – log 2 d) log 5 3 4x 2 (1/3)(log 5 4 + 2log 5 x)

17
EX: Write as one log: 3 log 2 t + ½ log 2 5 – 4 log 2 v log 2 (t 3 5 /v 4 ) (1/4)(log 2 3t + log 2 5v) log 2 ( 4 15tv)

18
Solve 2 x = 2 x = 2 -4 x = -4 64 x – 4 = (½) 2x (2 6 ) x – 4 = (2 -1 ) 2x 6x – 24 = -2x 8x = 24 x = 3

19
Solve (¾) 2x = 64 27 (¾) 2x = (27) -1 (64) (¾) 2x = (3 3 ) -1 (4 3 ) 2x = -3 x = -3 2 e 3x = e 7x – 2 3x = 7x – 2 -4x = -2 x = ½

20
Solve log n 1 = 2 25 n 2 = 1 25 n = 1 5 log √2 t = 6 ( 2 ) 6 = t 64 = t or (2 1/2 ) 6 = t t = 8

21
Solve log 2 x 3 = 6 2 6 = x 3 64 = x 3 or (2 6 ) 1/3 = (x 3 ) 1/3 4 = x ln (3x – 5) = 0 log e (3x – 5) = 0 e 0 = 3x – 5 1 = 3x – 5 6 = 3x 2 = x

Similar presentations

Presentation is loading. Please wait....

OK

Expanding and Condensing Logarithms Product Property.

Expanding and Condensing Logarithms Product Property.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on conservation of electricity Ppt online open house Ppt on law against child marriage pictures Ppt on yoga and meditation Ppt on expository text for kids Ppt on fire extinguisher types for servers Ppt on articles of association template Ppt on japanese tea ceremony Ppt on aircraft emergencies Pdf to ppt online converter without email