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Algebra 2
Chapter 7 Review: Exponential & Logarithmic Functions
Name:
Tell whether the function represents exponential growth or exponential decay.
1.
2.
1 5
f x   
2 7
x
1 7
f x   
3 5 
3.
x
f  x   3 4 
x
4.
5.
6.
1
f  x   e5x
5
1
f  x   e x
2
f  x   2e3x
Explain how the graph of g can be obtained from the graph of f.
f  x   3x
f  x   10 x
7.
8.
g  x   3x  5  4
g  x   10 x 2
Simplify the expression.
9.
10 x
10.
64e
e
e
x 1
e 4e 2
11. 5
e
e7
12.  3e4 
2
Graph the function. Give the asymptote, domain, and range.
13. f  x   3
x 2
1
3
14. f  x    
5
x 1
3
15. f  x   1  log2  x  2
Asymptote:
Asymptote:
Asymptote:
Domain:
Domain:
Domain:
Range:
Range:
Range:
1
17. f  x   e2 x  1
2
16. f  x   ln x  1
18. f  x   e3x  1
Asymptote:
Asymptote:
Asymptote:
Domain:
Domain:
Domain:
Range:
Range:
Range:
Rewrite the equation in exponential form.
1
19. log 5  1
5
Rewrite the equation in logarithmic form
21. 73  343
Evaluate the logarithm without using a calculator.
1
23. log8 2
24. log 2
4
Find the inverse of the function.
27. f  x   log  x  1
28. f  x   3  log6 x
20. ln1  0
22. r t  w
25. log 1 125
5
29. f  x   5  ln x  3
Use the change of base formula and your calculator to evaluate the following.
31. log8 2000
32. log 1 5
33. log e 125
3
26. ln e5
30. y  4e x 1  3
Expand the expression.
x2y
34. log2
5z
Condense the expression.
2
36. log2 x  3log2 y
3
35. log
37.
1
log 4 x  log 4 z 
3
10
7 x
38. log3 4  2log3 x  log3 5  log3 w
Solve the equation. Round the result to three decimal places if necessary.
3
39.  23 x   1  10
40. 3e  x  4  13
41. 95 x  272 x 1
8
42. ln 5x  1  ln 3x  2
45. log4 x  log4  x  3  1
43. 9log3 x  4  11
44. 8  2  log2 3x
46. log x  log3  2
47. You invest $900 in an account that pays 4.5% annual interest. How much will you have in 12 years
if it is compounded daily? Continuously?
48. You deposit $2000 into an account that pays 2% annual interest compounded quarterly. How long
will it take for the balance to reach $2500?
49. You buy a new car for $22,000. The value of the car decreases by 12.5% each year. Write an
exponential model for the value V of the car after t years. What is the value of the car after 3 years?
When will the value of the car be $8,000?
50. You have inherited land that was purchased for $30,000 in 1960. The value V of the land increased
by approximately 5% per year. Write a model for the value of the land t years after 1960. What is the
approximate value of the land in the year 2010?
Use your calculator to find an exponential model for the data.
51.
x
1
2
3
4
5
y
3.6
8.64
20.736
49.766
119.439
6
286.654
7
687.971
Use the properties of logarithms to rewrite the expression in terms of log 3 and log 4.
Then use log 3 
and log 4 
to approximate the expression.
DO NOT USE A CALCULATOR!!!
4
52. log12
53. log
54. log16
27
8
1651.13