Mac 1140
Chapter 4
Practice for Test 3
NON-CALCULATOR, Part A
1
2. Write in exponential form: log 2    3
8
36  6
1. Write in logarithmic form:
Evaluate:
4. 5 log5 8
3. log 10
5. log44
3
Rewrite as a single logarithm. Simplify final answer if possible.
6. log x +
1
log( x  2) - 3log(x+4)
2
7. ln(x2 – 9) – ln (x - 3) + ln(x)
Rewrite as a sum or difference of logarithms.
 x2 y 

8. log 
 t 
9. ln (3  2 x )
10. Solve by addition.
x + 2y = 6
2x - y = -8
11. Solve by substitution.
2x2 – y = 8
y = -7x – 4
12. Solve.
2x2 – y2 = 1
x2 – 2y2 = -1
Graph: 13. x2 + y2 > 9
14a. x + 2y  4
y x 3
14b. y > x2 - 4
-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 100
7. log 1017
8. ln e43
9. log 2 8
11. log 4 2
12. log 50 + log 2
13. log 3 54 – log 3 2
15. eln 17
16. 10log 17
14. 2log 7
10. log 2 (1/4)
7
Solve:
17. 23x-5 = 16
18. 82x-5 = 16x
21. log 2 (x) + log 2 (x + 6) = 4
19. 3x = 19
20. log 3 (x + 2) = 4
22. log (x – 3) – log (x + 2) = log (5)
23. ln x = 7
24. ln (x – 2) = 7
26. 3x = 5(x – 1)
25. eln 17 = 2x
3x  9
27. logx64 = 3
2
28. 4x-3 = 8
29.
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) = 3x
34. 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?
(Graph & use one-to-one, horizontal line test.)
a. f(x) = x2 – 3x - 4
b. f(x) =
x3
36. Determine the inverse of:
a. f(x) = 3x - 5
(Procedure is on page 138.)
2x  3
b. f(x) =
3x  5
A CALCULATOR MAY BE USED ON THE REMAINDER OF THE PROBLEMS.
SET THE MODE TO FOUR DECIMAL PLACES.
Evaluate
1. ln 924
Solve:
4.
e3x - 2 = 10
2. log 924
3. log 7 924
5. -3x = 5
6. log (2x + 7) = -3
7. 3 – ln(x) = 2x – 5
9. y = x2
y = -x2 + 4
8. ex = ln (x)
10. y = x + 2
xy = 7
ANSWERS
Non-calculator portion, Part A:
1
1
1. log366 =
2. 2-3 =
2
8
8. 2log(x) + log (y) -
1
log(t)
2
3. 1
4. 8
9. ln 3 + xln2
13.
14a.
x x2
 7. ln (x2 + 3x)
6. log 
3 
 ( x  4) 
 1 15 
10. (-2,4) 11.  , , , (-4, 24) 12. (1,  1 ), (-1,  1 )
2 2 
14b.
5.
3
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)
9
1
27)4 28)
29)  2 30)
31) x = ln 25 32) –4 + log552
2
2
33) x
y
-1 1/3
0 1
1 3
2
9
34)
x
y
1/3 -1
1
0
3
1
9
2
34) exponential form 3y = x
35) b, because this function is
one-to-one; each y is paired
with exactly one x.
36a) f-1(x) =
x 5
3
36b) f-1(x) =
5x  3
2x  2
Calculator portion:
1) 6.8287
2) 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)