MATH 1314 TEST 4 FALL 2015
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
1) log 390
26
A) 1.1761
B) 0.5461
C) 4.0060
D) 1.8312
1)
Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
2) log (5x - 2) = 1
2)
3
12
12
3
A)
B) C)
D) 5
5
5
5
3) log (x + 2) = log (5x - 3)
5
A) 4
4) log (-4 - 2x) = 2
2
1
A) 4
5) log
4
5
B)
4
B) -4
B)
C) 4
125
5=3
D)
1
4
5)
15
4
C)
Write the equation in logarithmic form.
6) 5 3 = 125
A) log
3)
1
D)
4
4)
(7x - 7) = log (3x + 8)
4
A) 1
5
C)
3
B) log
3
1
4
C) log
125 = 5
D) no solution
5
125 = 3
D) log
5
3 = 125
6)
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.
7) log (x + 5) + log (x - 1) = 2
7)
4
4
A) {4}
B) {3}
C) {3, -7}
D) {-7}
8) log (2 + x) - log (x - 2) = log 3
3
A)
B) {4}
2
8)
C)
D) {-4}
Determine which two functions are inverses of each other.
x-5
x+5
g(x) = 3x - 5
h(x) =
9) f(x) =
3
3
A) f(x) and g(x)
9)
B) g(x) and h(x)
C) f(x) and h(x)
1
D) None
Use a calculator to solve the equation. Round the answer to the nearest hundredth.
x
10) 7 = 63
A) -2.13
B) 1.81
C) 2.13
x
11) 3 = 15
A) 2.46
B) -2.46
Write as a logarithm of a single expression.
12) ( log x - log y) + 5 log z
a
a
a
A) log
a
xz5 y
B) log
C) 0.41
10)
D) 0.47
11)
D) 2.47
12)
a
xz 5
y
C) log
2
x
a z5y
D) log
a
5xz
y
Graph the function.
13) f(x) = 3 x
13)
A)
B)
C)
D)
Use properties of logarithms to expand the logarithmic expression as much as possible.
14) log7 x2 (x - 7)
A) log7 (x3 + 49x)
B) 2 log7 x + log7 (x - 7)
C) 2(log7 x)(log7 (x - 7))
D) log7 2x + log7 (2x - 14)
3
14)
Find the inverse of the one-to-one function.
5x - 8
15) f(x) =
7
A) f-1 (x) =
7
5x + 8
15)
7x - 8
B) f-1 (x) =
5
7x + 8
C) f-1 (x) =
5
D) f-1 (x) =
7
5x - 8
Does the graph represent a function that has an inverse function?
16)
A) Yes
16)
B) No
Solve the problem.
17) Austin invested $12,000 in an account at 6% compounded quarterly. Find the amount in Austin's
account after a period of 6 years.
A) $17,154.03
B) $5154.03
C) $16,900.53
D) $17,022.23
Find the unknown value.
18) log5 25 = y
A) 5
18)
B) 2
C) 10
D) 25
Determine whether the given functions are inverses of each other.
x+2
, g(x) = 2x - 2
19) f(x) =
2
A) Yes
19)
B) No
Solve the equation without using a calculator.
(3x - 5 )
= 16
20) 2
A) 8
17)
B) 3
C) -3
4
D)
1
8
20)