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ALGEBRA 2B – FINAL EXAM REVIEW 2014 CHAPTERS 8 & 11 1. Write the equation in logarithmic form.
4
2 = 16
2. Evaluate the logarithm.
log
4
10
3. Write the logarithmic expression as a single logarithm.
6 logb x + 3 logb y
4. Expand the logarithm.
2 xy 3
log a 4
z
5. Use the properties of logarithms to evaluate the expression.
log 4 4 + log 4 64 − log 4 16
6. Solve the equation. Check your answer.
x
– 85 + 7.14 = 45
7. Evaluate
log 2 16
8. Solve the equation.
83x−1 = 20
9. Solve the equation. Check your answer.
log 3x + 5 = 3
10. Write the expression as a single natural logarithm.
3 ln 5 + 2 ln x
11. Use natural logarithms to solve the equation.
e2 x + 5 = 8 12. Solve for x: 21 + 2log2 x = 31 1
7
13. Evaluate: log 7 . 14. Use the change of base formula to identify the expression that is equivalent to: log16 7 . (a) log 7
log 16
(b) log 16
log 7 (c) 16 log 7 (d) log
15. Write as the logarithm of a single quantity: 3log 2 + log x − 2log y 16. Expand: ln(16 x)2 17. Write an exponential function
A.
B.
for a graph that includes (1, 15) and (0, 6).
C.
D.
18. Write the equation in logarithmic form.
A.
B.
C.
D.
Evaluate the logarithm.
19.
A. –3
B. 5
C. –4
D. 4
20.
A. 5
B. –5
C. 4
D. 3
21.
Write the equation
A.
B.
in exponential form.
C.
Write the expression as a single logarithm.
22.
A.
C.
B.
D.
23.
A.
C.
B.
D. none of these
24.
A.
B.
C.
D.
D.
16
7
25. Use the properties of logarithms to evaluate
A. 2
B. 4
C. 8
.
D. 41
26. Solve
A. 0.6616
D. 1.9091
27.
. Round to the nearest ten-thousandth.
B. 2.6466
C. 1.7509
Solve
.
A.
B.
C.
D.
28. Solve
A. –1.8847
.
B. –0.1069
C. 0.3375
D. 1.0378
29. Solve
A.
7
−
4
.
B. 495
2
C. 250
D. 990
30. Solve
A. 10.7722
. Round to the nearest ten-thousandth.
B. 5
C. 2.7826
31. Solve
A. 0.33
. Round to the nearest hundredth if necessary.
B. 0.04
C. 3
D. 27
32. Solve
A. 0.0090
. Round to the nearest ten-thousandth.
B. 0.3103
C. 3.2222
D. 111
33. Solve
A. 12.3308
B. 43.3013
34. Solve
A. –0.448
B. 0.327
D. 0.6309
. Round to the nearest ten-thousandth.
C. 86.6025
D. 1875
C. 0.067
D. –0.046
35. Use summation notation to write the series 2 + 4 + 6 + 8 + ... for 10 terms.
A.
B.
C.
D.
36. Evaluate the series
A. 26
.
B. 10
C. 16
D. –6
37. Evaluate the series
A. 125
.
B. 38
C. 210
D. 165
38. Find the 50th term of the sequence 5, –2, –9, –16, ...
A. –352
B. –343
C. –338
D. –331
39. Use summation notation to write the series 49 + 54 + 59 + ... for 14 terms.
A.
C.
B.
D.
40. Which is the graph of
?
A.
C.
y
–12
–8
12
8
8
4
4
–4
4
8
12 x
–8
–4
–4
–8
–8
–12
–12
D.
y
–8
–12
–4
B.
–12
y
12
12
8
8
4
4
4
8
12 x
8
12 x
4
8
12 x
y
12
–4
4
–12
–8
–4
–4
–4
–8
–8
–12
–12