Mac 1140Practice for Test 3
Chapter 4
NON-CALCULATOR, Part A
1. Write in logarithmic form: 2. Write in exponential form: log
Evaluate:
3. log 104. 55. log44
Rewrite as a single logarithm. Simplify final answer if possible.
6. log x + - 3log(x+4)7. ln(x2 – 9) – ln (x - 3) + ln(x)
Rewrite as a sum or difference of logarithms.8. log 9. ln (3
10. Solve by addition.11. Solve by substitution.12. Solve.
x + 2y = 6 2x2 – y = 8 2x2 – y2 = 1
2x - y = -8 y = -7x – 4 x2 – 2y2 = -1
Graph: 13. x2 + y2 > 9 14a. x + 2y 14b. y > x2 - 4 y -x + y < 2
NONCALCULATOR, Part B:
Sketch the graph. Identify the asymptotes, the coordinates of the translated x-intercept, and domain and range for each graph. . (You may check the graph on your calculator)
1. y = log (x)2. y = -3 + log3(x)3. y = log (x – 3)4. y =-2 + log4(x-3)5. y = 4 + ln (x + 2)
Evaluate:
6. log 1007. log 10178. ln e439. log 2 810. log 2 (1/4)
11. log 4 212. log 50 + log 213. log 3 54 – log 3 214. 2log 7
15. eln 1716. 10log 17
Solve:
17. 23x-5 = 1618. 82x-5 = 16x19. 3x = 1920. log 3 (x + 2) = 4
21. log 2 (x) + log 2 (x + 6) = 422. log (x – 3) – log (x + 2) = log (5) 23. ln x = 7
24. ln (x – 2) = 7 25. eln 17 = 2x 26. 3x = 5(x – 1)27. logx64 = 3
28. 4x-3 = 829. 30. 25x + 1 = 6 31. ex = 25 32. 5x+4 = 52
Graph by filling in a table and graphing points in the table (see tables in answers; check graphs on calculator.).
33. f(x) = 3x34. f(x) = log3x (Replace f(x) with y & rewrite in exponential
form first. Then select y-values and evaluate
for x.)
35. Which of the following functions has an inverse?36. Determine the inverse of:
(Graph & use one-to-one, horizontal line test.) a. f(x) = 3x - 5
(Procedure is on page 138.)
a. f(x) = x2 – 3x - 4b. f(x) = b. f(x) =
A CALCULATOR MAY BE USED ON THE REMAINDER OF THE PROBLEMS.
SET THE MODE TO FOUR DECIMAL PLACES.
Evaluate1. ln 9242. log 924 3. log 7 924
Solve: 4. e3x - 2 = 105. -3x = 56. log (2x + 7) = -3
7. 3 – ln(x) = 2x – 58. ex = ln (x)
9. y = x210. y = x + 2
y = -x2 + 4 xy = 7
ANSWERS
Non-calculator portion, Part A:
1. log366 = 2. 2-3 = 3. 1 4. 8 5. 6. log 7. ln (x2 + 3x)
8. 2log(x) + log (y) - log(t) 9. ln 3 + xln2 10. (-2,4) 11. , (-4, 24) 12. (1, ), (-1,)
13. 14a. 14b.
Non-calculator portion, Part B:
1. x=0, (1, 0), D = (0,), R = (- or all reals 2. x=0, (1, -3), D =(0,), R = (- or all reals
3. x = 3, (4, 0), D = (3, ), R = all reals 4. x = 3, (4, -2), D = (4, ), R = all reals 5. x =-2, (-1, 4),
D = (-2, ,R= all reals 6) 2 7) 17 8) 43 9) 3 10) –2 11) 1/2 12) 2 13) 3 14) 1 15) 17 16) 17 17) 3 18) 15/2 19) log3 19 20) 79
21) 2 (throw away –8)
22) No solution (throw away-13/4) 23) e7 24) e7 + 2 25) 17/2 26) –ln5/(ln3 – ln5) or ln 5/(ln5 – ln3)
27)4 28) 29) 30) 31) x = ln 25 32) –4 + log552
33) x y 34) x y 34) exponential form 3y = x 35) b, because this function is
-1 1/3 1/3 -1 one-to-one; each y is paired
0 1 1 0 with exactly one x.
1 3 3 1
2 9 9 2 36a) f-1(x) =
36b) f-1(x) =
Calculator portion:
1) 6.82872) 2.9657 3) 3.5093 4).8283 5) no solution 6) –3.4995 7) 3.3896 8) no solution
9) (1.4142, 2) 10) (1.8284, 3.8284), (-3.8284, -1.8284)