Download MAC 1105 - Practice Test 5

MAC 1105 - Practice Test 5
****Problems 1 - 24 should be done without the use of a calculator.
Change to logarithmic form.
1. 41/2 = 2
2. e0 = 1
Change to exponential form.
3. log2 8 = 3
Evaluate:
6. log5 25
4. ln 7.38 = 2
1
7. log 2
16
5. ln e
2
9. 125 3
8. log 1000
Simplify:
 2  3 
11a.  a 3  a 4 
  
10. 9
11b.

1
2
 
x5
x2
11c. 2x 5
3
11d. 5x0
12. Write as the sum or difference of logarithms of single variables:
13. Write an expression with a single log term: a. ln 2 + 3ln x
Solve:
14. a.
3x  2  1  4
b.
3
3x  2  1  4
2x+3 = 24x 19. e7x = e5 20 8 4 x  2 24
23. log2 x = 3
3
3x  2  5  4
17. f ( x)  3 x  3
2
Solve: 18.
b. log x - log (x - 2)
3x  2  5  4 b.
15. a.
Give the domain and range and sketch a graph:
16 a. f ( x)  x  3
b. f ( x)  7  4 x
x2 y
log
3z
21.
9 x  3x
2
22. 4x – 1 = 15
24. log 4 + log x = 1
****A CALCULATOR COULD BE USED ON PROBLEMS 25 - 37:
Solve using four decimal places:
25. 23x = 7
26. 2x-4 - 7 = 10
27. 4e3x-6 =12
Calculate to 4 decimal places. 29. log3 7
30. log15 246
28. ex-1 + 7 = 4
31. ln 15
32. log 37
33. What is the value of $5000 invested at 7% compounded continuously, for 8 years?
34. What is the value of $5000 invested at 7% compounded quarterly for 8 years?
35 – 37. Solve using four decimal places:
35. log x + 2 = 1.43
36. ln x = 2.47
37. log5 x = -2
*****38 – 55: MORE NON-CALCULATOR PROBLEMS
Simplify:
38. 4x0
39. 4x-3
40. (4x)-3
41. 1252/3
43. 91/495/4 44. –361/2
42. a3xa5x
45 - 55 Solve - Give exact answers (non-calculator)
45) log 3 x = 2
46) ln x = 2
47) ln (x - 4) + 2 = 7
48) 5log 3 x = 20
49) e x = 7
50) 7 x = e
51) 9 2 x = 27 4 x  3
52) log x + log 3 = 2
54) log x + log (x – 3 ) = 1
53) log x – log 3 = 2
55) log x + log ( x – 3 ) = log 28
56 – 63: More Calculator Practice:
56-61. Solve: Give 4 decimal places (calculator)
56) 3 x = 2
58) e x 5 = 20
57) e x + 5 = 20
59) log x + 2 =  1
60) log 3 ( x + 2 ) = 5
61)
e x2   4
62 – 63. For each function, give the equation of the vertical asymptote, the equation of the horizontal
asymptote, and sketch the graph – then check the graph on your calculator.
62) y =
4
x 3
63) f (x) =
Answers: 1) log4 2 =
1
2) ln1 = 0
2
3x  2
x3
3) 23 = 8
4) e2 = 7.38 5)1 6) 2
7) -4 8)3 9)25 10)
1
3
17
x
x2
14)a. 11/3 b. 29/3 15) a. no real solution b. 1/3 16) a. D: [3, ) R: [0,) b. D: (-,7/4] R: (0, )
5
17) D: (-,) R: (-,) (check your graphs on your calculator) 18) 1 19)
20)  2 21) 0 or 2
7
22) 2 23) 8 24) 5/2 25) .94 26) 8.09 27)2.37 28) no solution 29)1.7712 30) 2.0330
31) 2.7081
32) 1.5682 33)$8753.36 34) $8711.07 35) .2692 36) 11.8224 37) .0400
2
3
38) 4 39) 4/x 40) 1/64x3 41) 25 42) a8x 43) 96/4=93/2=27 44) -6 45) 9
46) e
11) a. a 12
5
b. x3 c. 8x15
d. 5 12) 2log x + log y – log 3 – log z 13) a. ln 2x3 b. log
4
47) e + 4
48) 3 or 81
49) ln 7
50) log 7 e
51) 9/8
52) 100/3 53) 300 54) 5

55) 7 56) .6309
57) 2.7081
58) 2.0043
59) .1 60) 241
61) no solution

62) x = 3, y = 0
63) x = 3, y = 3 (check graphs on calculator)
(054)