LESSON



Review

Exponents & Logarithms

Identify whether the following is growth or decay, the values for a and b and the y intercept.

1. j(x) ’ −2(0.5)x 2. p(x) ’ 4(1.4)x

Solve.

3. A certain car depreciates about 15% each year.

a. Write a function to model the depreciation

in value for a car valued at $20,000.

b. Graph the function.

c. Suppose the car was worth $20,000 in 2005.

What is the first year that the value of this car

will be worth less than half of that value?

Identify the inverse of the following functions.

4. f (x ) ’ 5x + 2 5. f (x ) ’ x + 6 6. [pic]

7. [pic] 8. [pic] 9. [pic]

Graph each function. Then write and graph its inverse.

10. f (x ) ’ 2x − 4 11. [pic]

Write each exponential equation in logarithmic form.

12. 3 7 ’ 2187 13. 12 2 ’ 144 14. 5 3 ’ 125

Write each logarithmic equation in exponential form.

15. log10 100,000 ’ 5 16. log4 1024 ’ 5 17. log9 729 ’ 3

Evaluate by using mental math.

18. log 1,000,000 19. log 10 20. log 1

Use the given x-values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function.

21. f (x ) ’ 2 x ; x ’ −2, −1, 0, 1, 2, 3, 4

Express as a single logarithm. Simplify, if possible.

22. log6 8 + log6 27 23. log3 6 + log3 13.5 24. log4 32 + log4 128

25. log2 1920 − log2 30 26. log3 486 − log3 2 27. log6 180 − log6 5

Simplify, if possible.

28. log4 16 29. log2 8 x+12 30. [pic]

Solve.

31. 35x ’ 272x + 1 32. 36x + 2 ’ 64x 33. 55x - 6 ’ 50

34. 163x ’ 64x + 9 35. 81x ’ 243x + 2 36. [pic]

37. log x − log 9 ’3 38. log x + log 4 ’1 39. log (x + 6) ’ log(5x − 2)

Solve.

40. Halle deposited $4000 into an account that earns 5% interest each year. The

growth of her investment can be expressed by the exponential equation

A ’ 4000 (1 + 0.05)t, where A is the amount in the account after t years. In how

many years will her account exceed $10,000?

From the question above – what is the amount Halle will have, after the same number of years if the compounding is:

a. Quarterly

b. Daily

c. Continuous

Write each transformed function.

41. The function f (x) ’ log x is reflected across the y-axis.

42. The function f (x) ’ 8x is vertically stretched by

a factor of 2.

43. The function f (x) ’ 3x is moved left 4 units and two units down.

44. The function f (x) ’ ln x is shifted 3 units right and reflected

across the x-axis.

a. Write the function that is shifted 3 units right.

b. Take your answer to part a and write a function that

reflects it across the x-axis.

Given the parent function f(x) = 2x : state the transformation, the y intercept and the asymptote of the new function.

45. g(x) = 2x – 3

46. g(x) = 2x+4

47. g(x) = -3*2x

Given the parent function f(x) = log x : state the transformation and the asymptote of the new function.

48. g(x) = log x + 2

49. g(x) = log (x+2)

50. g(x) = -3*log x

Simplify.

51. ln ex + 2 52. eln 2x 53. e7 ln x

54. ln e3x + 1 55. ln e 56. ln e2x + y

Solve.

57. Use the formula A ’ P ert to compute the total amount for an investment

of $4500 at 5% interest compounded continuously for 6 years.

Answers:

1. Decay, a= - 2 , b = .5 , y intercept = - 2

2. Growth, a = 4 , b = 1.4 , y intercept = 4

3. a. y ’ 20,000( 0.85)x

b. [pic]

c. 2010

4. f −1(x) ’ [pic] 5. f −1(x) ’ x − 6 6. f −1(x) ’ [pic]

7. f −1(x) ’ −12x 8. f −1(x) ’ 4x +12

9. [pic], or [pic]

10. [pic]

[pic]

11. [pic]

[pic]

12. log3 2187 ’ 7 13. log12 144 ’ 2 14. log5 125 ’ 3

15. 105 ’ 100,000 16. 45 ’ 1024 17. 93 ’ 729

18. 6 19. 1 20. 0

21. Domain: {x|x > 0}; range: all real numbers

[pic]

22. log6 216 ’ 3 23. log3 81 ’ 4 24. log4 4096 ’ 6

25. log2 64 ’ 6 26. log3 243 ’ 5 27. log6 36 ’ 2

28. 0 29. 3x + 36 30. 30

31. x ’ −3 32. x ’ 2 33. x ( 1.686

34. x ’ 9 35. x ’ −10 36. x ’ −2

37. x ’ 9000 38. x ’ 2.5 39. x ’ 2

40. 19 years

a. $10282.11

b. $10322.45

c. $10342.84

41. g(x) ’ log (−x)

42. g(x) ’ 2(8)x

43. g(x) ’ 3x+4 - 2

44. a. g(x) ’ ln (x - 3)

b. g(x) ’ −ln (x - 3)

45. Down 3, -2, -3

46. Left 4, 16, 0

47. Reflected across x & Vert Stretch by 3, -3, 0

48. Up 2, 0

49. Left 2, -2

50. Reflected across x & Vert Stretch by 3, 0

51. x + 2 52. 2x 53. x7

54. 3x + 1 55. 1 56. 2x + y

57. $6074.36

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