Name _______________________________________ Date __________________ Class __________________
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
________________________
7. f ( x )  
x
12
________________________
5. f (x )  x  6
________________________
8. f ( x ) 
x  12
4
________________________
6. f ( x )  x 
1
2
________________________
9. f ( x ) 
3x  1
6
________________________
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Holt McDougal Algebra 2
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Graph each function. Then write and graph its inverse.
10. f (x )  2x  4
11.
________________________________________
f (x) 
5
x 2
2
________________________________________
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
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Holt McDougal Algebra 2
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Express as a single logarithm. Simplify, if possible.
22. log6 8  log6 27
________________________
25. log2 1920  log2 30
________________________
23. log3 6  log3 13.5
24. log4 32  log4 128
________________________
26. log3 486  log3 2
________________________
27. log6 180  log6 5
________________________
________________________
Simplify, if possible.
28. log4 16
________________________
29. log2 8 x+12
30. 7log7 30
________________________
________________________
Solve.
31. 35x  272x + 1
________________________
34. 163x  64x + 9
________________________
37. log x  log 9 3
________________________
32. 36x + 2  64x
33. 55x - 6  50
________________________
35. 81x  243x + 2
________________________
 1
36.  
2
________________________
38. log x  log 4 1
3x
 82
________________________
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
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Holt McDougal Algebra 2
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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
________________________
3x + 1
54. ln e
________________________
52. eln 2x
________________________
55. ln e
________________________
53. e7 ln x
________________________
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.
________________________________________________________________________________________
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Holt McDougal Algebra 2
Name _______________________________________ Date __________________ Class __________________
Answers:
1.Decay, a= - 2 , b = .5 , y intercept = - 2
2. Growth, a = 4 , b = 1.4 , y intercept = 4
20,000( 0.85)x
3. a. y
b.
c. 2010
4. f 1(x) 
x2
5
7. f (x)  12x
9. f 1 x  
5. f 1(x)  x  6
6. f 1(x)  x 
1
2
8. f 1(x)  4x 12
6x  1
1
, or f 1 x   2x 
3
3
10. f 1 x  
1
x2
2
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Holt McDougal Algebra 2
Name _______________________________________ Date __________________ Class __________________
11. f 1 x  
2
 x  2
5
12. log3 2187  7
13. log12 144  2
14. log5 125  3
15. 10  100,000
16. 4  1024
17. 93  729
5
18. 6
5
19. 1
20. 0
21. Domain: {x|x  0}; range: all real numbers
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 
30. 30
32. x
33. x  1.686
31. x
3
34. x
9
35. x
37. x
9000
38. x
2
10
2.5
36. x
39. x
2
2
40. 19 years
a. $10282.11
b. $10322.45
c. $10342.84
41. g(x)
log ( x)
42. g(x)
2(8)x
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Holt McDougal Algebra 2
Name _______________________________________ Date __________________ Class __________________
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
54. 3x
52. 2x
55. 1
53. x7
56. 2x
y
57. $6074.36
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Holt McDougal Algebra 2