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!A P E X H I G H S C H O O L
1501 L A U R A D U N C A N R O A D
A P E X , N C 27502
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Unit 5: Exponents and Logs
Day1: Thurs 11/13
Simplifying monomials
with pos/neg exponents
P3-4 evens
HW: p3-4 odds
Day 2: Fri 11/14
Solving Exp Eq with Same
Base p5-6 evens
HW: p5-6 odds
Day 3: Mon 11/17
exp models p7-8
Day 4: Tues 11/18
Graphing Exp Functions
P9-10 1-8all
HW: p 11 all
Day 5: Wed 11/19
QUIZ 1
(covers days 1-4)
Day 6: Thurs 11/20
Intro to Log
P12
HW: p13
Day 7: Fri 11/21
Log properties
P14-15
HW: p16
Day 8: Mon 11/24
“e” and Ln
P17-18 evens
HW: p17-18 odds
Day 9: Tues 11/25
Quiz #2 days 6-8)
Solving equations with
Logs and Ln p 19 evens
HW: p 19 odds
Thanksgiving Break
Day 10: Mon 12/1
Log/Exp Applications
P20
HW: p21
Day 11: Tues 12/2
Graphing Logs p22 HW: p23
Day 12: Wed 12/3
QUIZ 3(days 9-11) HW: Review #1 odds
Pg 24-25
Day 13: Thurs 12/4
Review #1 odds p 24-25 Study for test!
Day 14: Fri 12/5
TEST EXP/LOGS
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Day 3: Finding the Best Exp Model for a Data Set
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a.) What profession would be interested in this information?
b.) Make a scatter plot for your data in the calculator.
c.) Does this look like an exponential graph?
d.) Find the best regression equation for the data.
e.) How well does this model fit the data?
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b.) Make a scatter plot for your data in the calculator.
c.) Does this look like an exponential graph?
d.) Find the best regression equation for the data.
e.) How well does this model fit the data?
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a.) What profession would be interested in this information?
b.) Make a scatter plot for your data in the calculator.
c.) Does this look more like an exponential graph?
d.) Find the best regression equation for the data.
e.) How well does this model fit the data?
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d.) Find the best regression equation for the data.
e.) How well does this model fit the data?
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Day 4 HW
Exponential Functions: Bacteria Growth or Decay
1.) Graph y = 2x 2.) Graph y =
x
2
1
y
x
y
x
Describe the following transformations for each of the following equations.
3.) y = 2x ! 3
+ 4 4.) y =
1
2
1!x
! 5
Graph the following:
5.) y = 2 (4x) 6.) y = 3
x + 2
y
x
y
x
7.) y = 3 x-1
+ 2 8.) y = -1 ( 2x)
!
12
Day 6: Logarithm Notes and Practice xb = a means logxa = b
I. Write in exponential form.
1. 38log2 ! 2. 4
38log16 ! 3. 481log3 !
4. 01log8 ! 5. 13
1log3 "! 6.
3
24log8 !
7. 225
1log5 "! 8. 481log
3
1 "!
9. 2
12log4 ! 10. 2100log10 !
II. Write in logarithmic form.
1. 2525 ! 5.
64
116 3
2
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2. 4381! 6. 125252
3
!
3. 160 ! 7. 93
12
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8. 32
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III. Find the logarithm. Find x.!"#$#$%#"&'(#)*+",-.*+(#)*/01
1. !1.log10 1. 481log !x 11. x!8log16
2. !01.log10 2. 110log !x 12. x!5.log2
3. !3log27 3. 216log !x 13. 4log2
!x
4. !9log27 4. 3125log !x 14. 6log3
!x
5. !16log8 5. 4log4 "!x 15. 2
13log !x
6. !5.log4 6. 2log6 "!x 16. 6
12log !x
7. !4
1log
2
1 7. 0log3 !x 17. x!8log2
8. !9log3
1 8. 3
2log8 !x 18. x!25log
5
9. !25log5
1 9. x!100log10 19. 4
13log !x
10. !10
2 2log 10. x!27log9 20. 3log4 "!x
13
Day 6: Simplify and Solve Logs HOMEWORK (Do all work on a separate sheet of paper!)
Write each equation in logarithmic form.
1. 53 = 125 2. 8127 3
4
!
Write each equation in exponential form.
3. 500001.0log10 "! 4. 2
1
3
6log
2
3 "!
Evaluate each expression.
5. 81log3 6. 0001.0log10
7. 16
1log 2 8. 27log
3
1
9. 1log9 10. 4log8
Solve each equation. (left/right/left!)
11. 2
3log4 !x 12. 416log "!y
13. 38
1log "!a 14.
2
1log7 "!n
15. 3
4log
5!y 16.
6
19log 3!x
Remember: get one log equal to one log with the same bases, then drop !"#$%&'($)*+$(&%,#$-&.$/01
17. )12(log)73(log 88 #!# xx 18. )4(log)208(log 77 !#x
19. )7(log)19(log 33 #!" xx 20. )12(log)9(log 1212 !"x
21. )(log)30(log 6
2
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2
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14
Day 7: Log Properties NOTES and practice
1.) log xy = log x + log y 2.) log = log x – log y 3.) log xm = m log x
4.) m log x = x 5.) change of base : logm n =
I. Express each logarithm as a sum or difference of simpler logarithmic expressions.
Assume that all variables represent positive numbers.
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11. 12.
Express as a single logarithm with coefficient 1.
13. 14. 15.
16. 17. 18.
II. Solve for x.
1. 2.
3. 4.
15
5. 6.
7. 8.
9. 10.
Given that and find:
11. 12. 13. 14.
15. 16. 17. 18.
Find the value of each expression.
19. 20. 21.
22. 23. 24.
Solve for x.
25. 26.
27. 28.
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17
Day 8: Natural Logs
The Natural Base e !"#$%&'()*#+,%&-. An irrational number, symbolized by the letter e, appears as the base in many applied exponential functions. This irrational
number is approximately equal to 2.72. More accurately, The number e is called the natural base.
The function is called the natural exponential function.
exx
x
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11
lim
I . Express in logarithmic form:
1. 102.33
= x 2. 10 x = 379.31 3. e
2.5 = 12.18
4. 5
1
e = 1.221 5. e-2
= 0.135 6. 649.1!e
I I . Express in exponential form:
7. Log 229 = 2.3598 8. Log .8033 = -.0951 9. ln 8 = 2.079
10. 39.14
1ln +! 11. ln .01 = -4.605 12. ln e = 1
I I I . Express as a single Logarithm.
13. ln 6 + ln 5 ! ln2 14. 6ln9ln2
1+ 15. 38ln
3
1(+ 16. 24ln
2
3(
I V . F ind the Log of each number using a calculator . (Round to four decimal places)
17. Log 95 18. Log .233 19. Log 6.437 x 10-9
20. Log 1.8519 21. ln 120 22. ln 690
23. 5
6ln 24. 3
2
84ln 25. ln 0
/0))1(%)2)32$3#$245&)45)67*8))9:')56)%23;0
26. Log x = 2.63 27. Log x = -.4089 28. Log x = 5.3
29. ln x = 2.208 30. ln x = 1.808 31. ln x = -.105
18
V I . Evaluate W I T H O U T USIN G A C A L C U L A T O R! 32. ln e 33. ln ( e
2 ) 34. ln 1
35. ln 0 36. ln e1
37. eln
38. ln (en ) 39.
7ln6ln !e 40. 7ln2 "e 41.
9ln2
18ln
3
1!
e
V I I . Simplify and then Evaluate. (Use a calculator only when necessary)
42. ln 48 ! 4 ln 2 43. 3ln212ln9ln2
1#! 44. $ % 3ln25ln45ln
2
1#!
45. 6ln8ln #e 46. ln 6 + ln 30 ! (ln 5 + 3 ln 2) 47. )3ln2ln5(8ln4ln
2
1!#!
48. 3 ln 4 ! (ln 2 + ln 8 ) 49. )3(ln
2
1
e
V I I I . Solve and Check! 50. Log (x + 2) + Log (x) = 1 51. Log (x + 3) - Log ( x ! 1) = 1 52. Log x = 2 - Log (x + 21)
I X . Solve by rewriting the problem in another form. Round decimal answers to four places!
53. ln x =3 54. 3
1ln &x 55. 5&xe
56. 5
3
ln ex & 57. 12ln &xe 58. 2
1ln #&x
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20
Day 10: Exp/Log Applications Notes and Practice
Growth/Decay : xaby ! Value of an Asset: " #xray $! 1
Continuously Compounded: rtPeA ! Half Life: y = a(.5) ht
Compound Interest:
n t
nrPA %&
'()
* +! 1
Solve each problem. 1. Suppose $500 is invested at 6% annual 2. Suppose $500 is invested at 6% annual interest compounded twice a year interest compounded continuously When will the investment be worth When will the investment be worth $1000? $1000? 3. An organism of a certain type can grow 4. For a certain strain of bacteria, b is from 30 to 180 organisms in 5 hours. 3 when t is measured in days. How Find b for the growth formula. long will it take 20 bacteria to increase to 2000? 5. An investment service promises to 6. A radioactive element has a half life triple your money in 12 years. of 30 years. If you have 6 g. now, Assuming continuous compounding of how much will be left in 100 years? interest, what rate of interest is needed? 7. A piece of machinery valued at 8. Dave bought a new car 8 years ago for $250,000 depreciates at 12% per year $5400. To buy a new car comparably by the fixed rate method. After how equipped now would cost $12,500. many years will the value have assuming a steady rate of increase, depreciated to $100,000? what was the yearly rate of inflation in car prices over the 8 year period?
21
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Day 11; HW!Graphing Logs
1. y = log4x 2. y= log4(x+5) 3. y = log4x +3
Use for #1,2, 3
4.) y = log2x 5. y = log2x -3 6. y = log2(x-4)
Use for #4,5,6
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