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Alg 2 Chapter 6

Total questions: 91

Worksheet time: 5hrs 16mins

Name
Class
Date
1.
Find the inverse of f(x)=log4(x+4)
a)
f-1(x)=4(x-4)
b)
f-1(x)=4x+4
c)
f-1(x)=4x-4
d)
f-1(x)=4x
2.
Find the inverse of the function f(x)=5(x+2)
a)
f-1(x)=log5(x-2)
b)
f-1(x)=log5(x)-2
c)
f-1(x)=log5(x)+2
d)
f-1(x)=log5(x+2)
3.
Convert log(x)=5 to exponential form
a)
15=x
b)
10x=5
c)
x5=10
d)
105=x
4.
Convert 6(x+2)=216 to logarithmic form
a)
log216(x+2)=6
b)
log6(x+2)=216
c)
log6(216)=x+2
d)
log(x+2)(216)=6
5.
Find the inverse of the function f(x)=4(x+1)-1
a)
f-1(x)=log4(x+1)-1
b)
f-1(x)=log4(x-1)+1
c)
f-1(x)=log4(y+1)-1
d)
f-1(x)=log4(x)
6.
Convert log8(x+2)=3 to exponential form.
a)
8(x+2)=3
b)
3(x+2)=8
c)
83=x+2
d)
38=x+2
7.
Find the inverse of f(x)=log3(x+2)
a)
f-1(x)=1x
b)
f-1(x)=3x-2
c)
f-1(x)=3(x-2)
d)
f-1(x)=3(x+2)
8.
Convert 10(x+5)=100 to logarithmic form.
a)
log100=x+5
b)
log(x+5)=100
c)
log(100)=x+5
d)
log(x+5)(100)=10
9.
Find the inverse of f(x)=2log3(x)
a)
f-1(x)=3(x/2)
b)
f-1(x)=(3x)/2
c)
f-1(x)=3x
d)
f-1(x)=3(x-2)
10.
What is the inverse of f(x)=5x+3?
a)
f-1(x)=log3(x-5)
b)
f-1(x)=log5(x)-3
c)
f-1(x)=log5(x-3)
d)
f-1(x)=log5(x+3)
11.
Which of the following function is the inverse of f(x)=⅓x-1?
a)
g(x)=3x+1
b)
g(x)=⅓(x+1)
c)
g(x)=3x+3
d)
g(x)=3x-1
12.
Convert log(x)=y+2 to exponential form.
a)
10(y+2)=x
b)
1x=y+2
c)
10x=y+2
d)
x(y+2)=10
13.
Convert 2x+6=10 to logarithmic form
a)
log4(x)=2
b)
log2(4)=x
c)
log2(10)=6
d)
log2(x)=4
14.
Solve for x.
logx(64)=3
a)
x=8
b)
x=4
c)
x=3
d)
x=64
15.
Convert log12(x)=2 to exponential form.
a)
122=x
b)
12x=2
c)
x2=12
d)
2x=12
16.
Find the inverse of the function f(x)=log3(x)+5
a)
f-1(x)=3x-5
b)
f-1(x)=3(x+5)
c)
f-1(x)=3(x-5)
d)
f-1(x)=3x+5
17.

Write in exponential form:

log 2 32 = 5

a)

25 = 32

b)

52 = 32

c)

532 = 2

d)

232 = 5

18.
Write in exponential form:
log 36 1 = 0
a)
360 = 1
b)
361 = 0
c)
136 = 0
d)
10 = 36
19.
Write in exponential form:
log 3 6561 = 8
a)
38 = 6561
b)
83 = 6561
c)
36561 = 8
d)
86561 = 3
20.
Write in logarithmic form:
92 = 81
a)
log 9 81 = 2
b)
log 2 81 = 9
c)
log 9 2 = 81
d)
log 2 9 = 81
21.
Write in logarithmic form:
45 = 1024
a)
log 4 1024 = 5
b)
log 5 1024 = 4
c)
log 4 5 = 1024
d)
log 5 4 = 1024
22.

Evaluate log525 = x

a)

2

b)

5

c)

125

23.

Evaluate log41 = x

a)

1

b)

0

c)

4

d)

undefined

24.
Log with a base "e" (loge) is the same thing as...
a)
"e"
b)
Natural Logarithm (LN)
c)
Common Logarithm (Log)
d)
Natural Log, base "e"
LNe
25.

Rewrite ex = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

logx e = 9

d)

log9 x = e

26.
Rewrite the equation in logarithmic form.
a)
A
b)
B
c)
C
d)
D
27.
Rewrite the equation in logarithmic form.
a)
A
b)
B
c)
C
d)
D
28.
Rewrite in exponential form.
a)
A
b)
B
c)
C
d)
D
29.
Rewrite in exponential form.
a)
A
b)
B
c)
C
d)
D
30.

Convert between logarithmic and exponential form


[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

31.

Convert between logarithmic and exponential form


[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

32.

Convert between logarithmic and exponential form


[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

33.

Convert between logarithmic and exponential form


[Click on the image if you need to make it larger]

a)

A

b)

B

c)

C

d)

D

34.

Rewrite each equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

35.
Rewrite logvn = a in exponential form.
a)
va = n
b)
na = v
c)
vn = a
d)
an = v
36.

Rewrite log28 = 3 in exponential form

a)

28 = 3

b)

23 = 8

c)

32 = 8

d)

83 = 2

37.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
38.
Rewrite logpt = m in exponential form.
a)
pt = m
b)
tm = p
c)
mt = p
d)
pm = t
39.
Solve for x.
5x = 1
a)
0
b)
-1
c)
2
d)
1
40.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
41.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
42.
Write logb(x/y) as two logs
a)
logbx-logby
b)
logbx+logby
c)
logbx*logby
d)
logbx/logby
43.
Write logb(xy) as two logs
a)
logbx+logby
b)
logbx-logby
c)
logbx*logby
d)
logbx/logby
44.

Write as a single log: log(12) + 2 log(x)

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x2)

45.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
46.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
47.

Solve each equation. Round your answers to the nearest ten-thousandth.

a)

19.1474

b)

.9688

c)

.0971

d)

-9.0312

48.

Solve the equation. Round your answers to the nearest ten-thousandth.

a)

.5573

b)

5.5732

c)

-.5573

d)

55.7321

49.

Solve each equation. Round your answers to the nearest ten-thousandth.

a)

9.8741

b)

-.4231

c)

-.0844

d)

8.0388

50.

Evaluate.

log6 (1/216) = x

a)

3

b)

1/3

c)

-1/3

d)

-3

51.
Write in logarithmic form.
2-4 = 1/16
a)
log2(1/16) = -4
b)
log-4(1/16) = 2
c)
log -4 2 = 1/16
d)
log2(-4) = 1/16
52.

Determine whether the function represents exponential growth or exponential decay

a)

Exponential Growth

b)

Exponential Decay

53.
Write in exponential form.
log232 = 5
a)
2-5 = 32
b)
232 = 5
c)
25 = 32
d)
325 = 2
54.

Determine whether the function represents exponential growth or exponential decay

a)

Exponential growth

b)

Exponential decay

55.

Determine the equation of the asymptote?

a)

x=3

b)

x=4

c)

y=-4

d)

y=4

56.

Determine whether the function represents exponential growth or exponential decay

a)

Exponential growth

b)

Exponential decay

57.

Determine the equation of the asymptote?

a)

x=5

b)

y=-5

c)

y=2

d)

x=-5

58.

When you get stuck in the logarithmic form, you switch to

a)

Natural logarithm form

b)

Exponential form

c)

Common logarithm

d)

Logarithm base b

59.

Solve for y

a)

y = log 3/ log 4

b)

y = log 4/ log 4

c)

y = log 4/ log 3

d)

y = log 3/ log 3

60.

When you want to find the inverse of a function, you first

a)

Solve for y

b)

Change to exponential form

c)

Switch x and y

d)

Change to logarithmic form

61.

What is the next step to solve for x

a)

Divide both sides by e

b)

Do nothing

c)

Take the natural log of both sides

62.
Chip invested $5,000 in a corporate bond which pays 8.25% interest compounded quarterly.  How much money will Chip have in 15 years for retirement?
a)
$6,187.50
b)
$17,019.32
c)
$17,234.93
d)
$6,791.46
63.
Zachary invested $7,500 in a C.D. (certificate of deposit) at Bank of America.  It earns 11% interest compounded continuously.  How long will it take for Zachary's investment to triple?
Round to 2 d.p. 
a)
87.42 years
b)
.10 years  (one-tenth of a year)
c)
9.99 years
d)
4.34 years
64.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).

a)

604

b)

777

c)

29

d)

198

65.

The population of Boringtown decreased annually by 1.8% between the year 2015-2018. In 2015, there were approximately 200,000 people living in Boringtown. Which function models the city's population since 2015?

a)

y = 200,000(1 + 0.018)3

b)

y = 200,000(1 - 0.18)3

c)

y = 200,000(1 + 0.18)3

d)

y = 200,000(1 - 0.018)3

66.

Your shiny new boat cost $7650. The depreciation for your boat is 14% per year. You want to know the value of your boat in 3 years. What is the equation that models this problem?

a)

y = 7650(1 + 0.14)3

b)

y = 7650(1 - 0.14)3

c)

y = 7650e(0.14)(3)

d)

y = 7650 (1 + 0.14/12)(12)(3)

67.

Solve for x

a)

0.75

b)

3

c)

0.667

d)

1.5

68.

lnx = -3

a)

8.1548

b)

-8.1548

c)

0.0498

d)

-0.0498

69.
Rewrite in exponential form:
ln(2) = x
a)
2x = 10
b)
102 = x
c)
ex = 2
d)
e2 = x
70.

Solve for x
5(7x)+20=1255\left(7^x\right)+20=125  

a)

1.827

b)

.827

c)

.056

d)

1.565

71.

Solve the equation. Round your answer to the nearest ten-thousandth. −7(10x)=−54-7\left(10^x\right)=-54  

a)

2.0431

b)

1.7481

c)

1.7254

d)

0.8873

72.
log525 = ?
a)
2
b)
5
c)
125
d)
10
73.
Solve:
log (4x − 5) = log (2x − 1) 
a)
0
b)
1
c)
2
d)
3
74.

Solve for x:

32x=27(x+1)3^{2x}=27^{\left(x+1\right)}  

a)

x=6

b)

x=0

c)

x=3

d)

x=-3

75.
List the range for the following.
a)
(-∞,∞)
b)
(-1, ∞)
c)
(5,∞)
d)
(1, ∞)
76.
Find the asymptote for the following.
a)
x = -1
b)
x = 1
c)
y = 5
d)
y = -5
77.
Match the graph with its equation
a)
y = log4 (x)+2
b)
y = log4 (x + 2) + 1 
c)
y = log4 (x - 1) + 2
d)
y = log4 (-x + 2)
78.

Given  y=3xy=3^x  determine the y-intercept 

a)

(0,1)

b)

(0,3)

c)

(1,0)

d)

(3,0)

79.
What is the range of the function
𝑓(𝑥)=4𝑥−1+3?
a)
(3, ∞)
b)
(-∞, ∞)
c)
(1, ∞)
d)
(-∞, 3)
80.
What is the domain of the function
𝑓(𝑥)=log(𝑥+1)−3?
a)
(-∞, ∞)
b)
(-3, ∞)
c)
(-1, ∞)
d)
(-∞, -1)
81.

Solve the following

log11(x) - log11(x-1) = log11(6)

a)

6/5

b)

5

c)

6

d)

-1/2

82.

What is the x-intercept of log⁡6(x)−1\log_6\left(x\right)-1  

a)

(6, 0)

b)

(0, -3)

c)

(0, 6)

d)

(-3, 0)

83.

Describe the transformations of f(x) = -log2(x + 1)

a)

left 1 & compress

b)

left one & reflect over the y-axis

c)

left one & reflect over the x-axis

d)

right one & reflect over the x axis

84.
What are the transformations of this graph?
a)
Right 1 Up 5
b)
Right 1 Down 5
c)
Left 1 Up 5
d)
Left 1 Down 5
85.
Expand
a)
6log8v-2log8u
b)
6log8u-2log8v
c)
3log8u-2log8v
d)
6log8u+2log8v
86.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (12 * 2x)
d)
log (12x2)
87.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
88.
What equation matches the graph?
a)
f(x) = 3x
b)
f(x) = (⅓)x
c)
f(x) = log₃(x)
89.
Which equation matches the graph?
a)
y = 2x+3
b)
y = 2x + 3
c)
y = 2x
d)
y = 2-x
90.

The number of bacteria in the colony grows continuously. The colony began with a population of 4000. In three days the population doubles.

What is the daily rate?

a)

20%

b)

23%

c)

77%

d)

80%

91.

Simplify the expression 

eln⁡30e^{\ln30}  

a)

e

b)

30

c)

e30e^{30}  

d)

30e

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