Download Exam 4 MAC 1105 Summer 2011

Exam 4 MAC 1105 Summer 2011
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the function.
1) Use the graph of f(x) = 3 x to obtain the graph of g(x) = 3 x + 2 - 1.
6
1)
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
A)
B)
6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
y
2
4
6 x
2
4
6 x
D)
6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
Graph the function by making a table of coordinates.
A‐1
y
2) f(x) = 3 x
4
2)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
A)
B)
6
6
y
y
4
4
2
2
-6
-6
-4
-2
2
4
-4
-2
6 x
2
4
6 x
2
4
6 x
-2
-2
-4
-4
-6
-6
C)
D)
6
6
y
y
4
4
2
2
-6
-6
-4
-2
2
4
6 x
-4
-2
-2
-2
-4
-4
-6
-6
Write the equation in its equivalent exponential form.
3) log x = 3
2
A) 2 3 = x
B) x3 = 2
4) log 27 = 3
b
A) 273 = b
3)
C) 3 2 = x
D) 2 x = 3
4)
C) b3 = 27
B) 3 b = 27
A‐2
D) 27b = 3
5) log 216 = x
6
A) 6 x = 216
5)
B) 216 6 = x
C) x6 = 216
D) 216 x = 6
B) log y = 3
5
C) log
D) log 3 = 5
y
7) d3 = 1331
A) logd 3 = 1331
B) log3 1331 = d
C) logd 1331 = 3
D) log1331 d = 3
8) 6 x = 216
A) log
B) log
C) log
216 = 6
D) log 216 = x
6
Write the equation in its equivalent logarithmic form.
6) 5 3 = y
A) log 5 = 3
y
6)
3
y = 5
7)
8)
216
6 = x
216
x = 6
x
Evaluate the expression without using a calculator.
9) log6 36
A) 12
10) log
B) 36
D) 6
10)
B)
1
2
C) 1
D)
1
10
1
3 27
A)
12) log
C) 2
10
10
A) 10
11) log
9)
1
3
27
11)
B) -3
C) 3
D) 9
12)
3
A) 9
13) log10 A) - B) 1
C)
1
3
D) 3
1
10
1
10
13)
B) -
1
2
C)
Find the domain of the logarithmic function.
14) f(x) = log (x - 5)
9
A) (-∞, 5) or (5, ∞)
B) (5, ∞)
1
10
D)
1
2
14)
C) (-∞, 0) or (0, ∞)
A‐3
D) (-5, ∞)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
x5
15) log
15)
4 y6
A) 6 log y - 5 log x
4
4
B) 5 log x + 6 log y
4
4
C) 5 log x - 6 log y
4
4
D)
16) loga x
5
log ( )
4
y
6
3
x4 x + 5
(x -2)2
16)
1
A) 4 loga x + loga (x + 5) - 2 loga (x - 2)
3
B) loga x4 + loga (x + 5)1/3 - loga (x - 2)2
C) 4 loga x - 3 loga (x + 5) - 2 loga ( x - 2)
D) loga x4 + loga (x + 5)-3 - loga (x - 2)2
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
17) log 12 - log 4
17)
3
3
A) log 48
B) 1
C) log 8
D) log 12 1/4
3
3
3
18)
1
log6 x + log6 y
2
A) log6
19)
x
y
18)
x
C) log6
y
B) log6 y x
D) log6 xy
1
(log2 x + log2 y) - 6 log2 (x + 9)
3
3
3
A) log2 xy
6(x + 9)
19)
B) log2 3
xy
C) log2 (x + 9)6
3
x + y
(x + 9)6
3
D) log2 x + y
(x + 9)6
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
20) log 6
10
A) 1.2851
B) 0.7782
C) 1.7782
D) -0.2218
Solve the equation by expressing each side as a power of the same base and then equating exponents.
21) 3 (1 + 2x) = 27
A) {-1}
B) {9}
C) {3}
D) {1}
22) 16x + 2 = 64x - 7
A) {11}
B) {25}
C) {23}
D) {9}
20)
21)
22)
A‐4
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
23) ex = 4.2
23)
A) 1.44
B) 66.86
C) 11.42
D) 0.62
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
24)
24) log (x - 1) + log (x - 7) = 3
3
3
B) {11}
C) {-2}
D) {10}
A) {10, -2}
25) log
(x - 2) = 1 - log x
15
15
A) {3}
B) {-5}
25)
C) {-3}
A‐5
D) {5}
Answer Key
Testname: EXAM4
1) C
2) B
3) A
4) C
5) A
6) B
7) C
8) D
9) C
10) B
11) B
12) C
13) B
14) B
15) C
16) A
17) B
18) B
19) B
20) B
21) D
22) B
23) A
24) D
25) D
A‐6