PRECALC I – SECTION 6.5 WORKSHEET USING PROPERTIES OF LOGS ...

[Pages:9]PRECALC I ? SECTION 6.5 WORKSHEET

USING PROPERTIES OF LOGS

EXPRESS THE FOLLOWING IN TERMS OF a, b, and c,

GIVEN: log 2 = a

log 3 = b

log 5 = c

1. log 4 =

2.log 25 =

3. log 10 =

4. log 6 =

5.log 15 = 6. log 9 =

5

7. log 4 3 =

8. log 3 25 =

9. log 2 = 35

10. log 6 =

Name ________________________________

Simplify WITHOUT a calculator:

2

1. 10003

2. 3 9i 6 9

Logarithm Practice Worksheet 3. log3 9

( )3

4. 4 3

5. log9 3

6. log4 8

- 2

7. 32 5

8. log10 .0001

( )( ) 9. 62- 61+

10. log2 8

11. log8 ?

12. log9 27

13. log8 4 2

14. log4 x = 3

Suppose f(x) = 1 ? x3 and g(x) = 2x ? 3. Find the following:

16. f(g(1))

17. g(f(-1))

19. g-1(0)

20. f(f-1(4))

15.

logx 8 =

3 4

18. f-1(9) 21. g-1(f-1(0))

If log 5 = a and log 4 = b, express the logarithm in terms of a and b. Ex. log 16 = log 42 = 2log 4 = 2b

22. log 4 16

23. log 20

24. log 1.25

25. log 2

26. log 10

27. log 1 25

28. log 250

29. log 10

30. log 3 50

Let x = log 2, y = log 3, and z = log 10. Express each logarithm in terms of x, y, and z.

31. log 6

32. log 9

33. log 5

34. log 18

35. log 1.5

36. log .75

37. log 80

38. log 30

39. log .0006

40. log 9 2

41. log 1200

Let log a = 2, log b = 3, and log c = 4. Evaluate each logarithm.

42. log a2b

43. 3 bc2

44. log a bc

45. log 6 a2b3c

46. log a3b2 c 4

Simplify to help you solve each equation. 48. log3 x + log3 1 = 0

5

47. log a2 bc 2

49. 2log4 y = 3

50. If log8 5 = a, then log8 1 = _________ 5

LOGARITHMS PRACTICE WORKSHEET NO CALCULATORS!!!

Find each logarithm: 1. log2 64

4. log 104

2. log4 2

1 5. log1/3 81

3.

log4

1 16

6. log1/4 64

Find the value of x in each equation: 7. logx 625 = 4

13. log (x2 + 9x) = 1

8. log25 x = ?

14. log (4x ? 4) = 2

9. log1/2 x = -6

15. log5 x = 3 log5 7

10. logx .1 = -1

16. log2 x = ? log2 81

11. logx 125 = -3

17. log5 x = 2 log5 7

12. log3 27 = x

1

18.

log10 x =

(2 log 4 + 2 log 2) 6

Express each logarithm as the sum or difference of simpler logs: 19. log2 (xy) = 20. log2 (abc) = 21. loga 2x1/2 = 22. loga (bc)2 =

23. loga bc =

24.

logb (

x )= y

Express each as a single logarithm with a coefficient of 1: 25. loga x + loga y ? loga z =

26. 2 loga x ? ? loga y =

27. 2(loga z ? loga 3) =

Simplify (WITHOUT A CALCULATOR): 28. log6 2 + log6 3

29. log5 200 ? log5 8

30. log 85 ? log 17 + ? log 400

Chapter 6 Guided Notes

Halldorson

PRECALC I CHAPTER 6 STUDY GUIDE

2009-2010

1. Know how to simplify exponential and logarithmic expressions with and without a calculator. (#1-8, 17-22, 25, 26)

2. Know the properties of logs. (#37-43, 47, 48)

3. Be able to solve equations. (#13-16)

4. Know what the graphs exponential and logarithmic functions look like. Know the characteristics, like domain, range, asymptotes. (#30, 32-34, 69, 70)

5. Be able to give formulas in terms of another variable and then substitute in values. (#55a, 56, 59, 62)

6. Be able to solve compound interest problems and population problems. (#58, 60)

PRECALC I ? CHAPTER 6 REVIEW WORKSHEET

SIMPLIFY EACH OF THE FOLLOWING WITHOUT A CALCULATOR

1. 3245

2. 2743

1

-

1 2

3. 25

8 -23 4. 27

5. log6 1

6. ln e10

7.

log(

1 5

)

25

8.

log

8

2

9.

log

9

1 27

( ) 10.

x6 y15

(

1 3

)

1

Chapter 6 Guided Notes

Halldorson

2009-2010

EXPRESS EACH OF THE GIVEN LOGARITHMS AS THE SUM AND/OR DIFFERENCE OF SIMPLIER LOGS, WITHOUT ANY RADICALS OR EXPONENTS

( ) 11. log ab3c

x 12. ln y2

EXPRESS EACH OF THE FOLLOWING AS A SINGLE LOGARITHM WITH A COEFFICIENT OF ONE

13. log x + log y - 3log z

14. 2 (ln p - ln 3)

15. Express this equation without logs: log x - log y = log 5 + log w - 2 log z

16. Determine the value of x (correct to the nearest thousandth): ln x = 2

17.

Determine the exact value of x:

log27

x

=

-4 3

18. Determine the exact value of m: logm 8 = 6

MATCH EACH EQUATION WITH ITS GRAPH

19. f (x) = - ln x

4 2

20. g(x) = 2x

4 2

21. h(x) = log2 x

4 2 5

-2

a.

-2

b.

-4

-2

c.

22. r(x) = (0.2)x

4 2

5 -2

d.

2

Chapter 6 Guided Notes

Halldorson

2009-2010

23. Matt invested $1,000.00 in an account paying 7.5% interest. Determine his balance after four years if interest is:

a. compounded monthly

b. compounded continuously

24. Nicole has invested $5000 in an account paying 6.25% interest compounded continuously. How long before her investment doubles in value?

25. In 1995 the population of Mexico was estimated at 94,800,000 with an annual growth rate of 1.85%. Assuming continuous growth at this rate, estimate the population of Mexico in the year 2010.

26. The population of Peru in 1998 was estimated at 18,4000,000 with an annual average growth rate of 2.7%. Assuming continuous growth at this rate, in what year would the population reach 30,000,000.

SOLVE EACH OF THE EQUATIONS

27. log6(9x + 4) = log619

28. 4x = 8

29. 25x+2 = 1 x 25

30. 92x+1 = 27 x+2

31. log x - 4 log 5 = -2

32. ln(x -1) - ln(x + 1) = -2

FOR EACH OF THE GIVN FUNCTIONS: a). DRAW AN ACCURATE GRAPH, b). STATE THE DOMAIN, c). STATE THE RANGE, AND d). STATE THE EQUATION OF ANY ASYMPTOTE(S).

33. g(x) = log3 x

34. r(x) = 4x

10 8 6 4 2

-10

-5

-2

-4

-6

-8

5

10

10 8 6 4 2

-10

-5

-2

-4

-6

-8

5

10

3

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