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WorksheetsCommon Logarithms
Total questions: 58
Worksheet time: 2hrs 0mins
Name
Class
Date
1.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
2.
True or False: log₈64=2
a)
True
b)
False
3.
The base of common log is 10. So log 100 = ?
a)
1
b)
2
c)
10
d)
50
4.
log1000
a)
1
b)
2
c)
3
d)
4
5.
log525 = ?
a)
2
b)
5
c)
125
6.
Evaluate.
log381
log381
a)
4
b)
1/4
c)
-4
d)
-1/4
7.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions
c)
Quadratic Functions
d)
Polynomial Functions
8.
log 10 =
a)
1
b)
2
c)
3
d)
4
9.
log 100 =
a)
1
b)
2
c)
3
d)
4
10.
log 0.1 =
a)
-2
b)
-1
c)
1
d)
2
11.
log 100 - log 1000 =
a)
1
b)
2
c)
-1
d)
-2
12.
log 1000 - log 0.01 =
a)
2
b)
3
c)
4
d)
5
13.
log (1/10) =
a)
-2
b)
-1
c)
1
d)
2
14.
log (1/1000) =
a)
-3
b)
-2
c)
-1
d)
3
15.
log 100 + log 0.1 =
a)
100.1
b)
3
c)
2
d)
1
16.
log 1003 =
a)
3
b)
4
c)
5
d)
6
17.
log 10(1/2) =
a)
1/2
b)
1/3
c)
1
d)
2
18.
log (1/100) - log (1/1000)
a)
-2
b)
-1
c)
1
d)
2
19.
log 100000 =
a)
6
b)
5
c)
4
d)
3
20.
log 1 =
a)
-2
b)
-1
c)
0
d)
1
21.
log 1000 + log 0.1 - log 0.01 =
a)
0
b)
2
c)
3
d)
4
22.
log √10
a)
1/2
b)
-1
c)
2
d)
1
23.
log 100√10
a)
1/2
b)
3/2
c)
5/2
d)
2
24.
log √1000 =
a)
1/2
b)
3/2
c)
5/2
d)
2
25.
log 100 - log √10 =
a)
1/2
b)
3/2
c)
5/2
d)
2
26.
Use a calculator to evaluate log 6
a)
-1.30
b)
.7781
c)
-1.25
d)
.80
27.
Use a calculator to evaluate log 25
a)
1.397
b)
1.598
c)
-1.397
d)
.80
28.
Rewrite as an exponential:
log(10,000)=4.
log(10,000)=4.
a)
e4=10,000
b)
410,000=10
c)
104=10,000
d)
04=10
29.
Rewrite log28 = 3 in exponential form/
a)
28 = 3
b)
23 = 8
c)
32 = 8
d)
83 = 2
30.
Rewrite 34 = 81 in logarithmic form.
a)
log34 = 81
b)
log813 = 4
c)
log381 = 4
d)
log481 = 3
31.
Classify the following graph.
a)
Exponential Growth
b)
Exponential Decay
c)
Logarithmic
32.
Classify the following graph.
a)
Exponential Growth
b)
Exponential Decay
c)
Logarithmic
33.
Change to Exponential Form:
log636 = 2
log636 = 2
a)
26=36
b)
62=36
c)
362=6
d)
366=2
34.
(-151)0
a)
0
b)
1
c)
-151
d)
151
35.
Does this graph represent exponential growth or decay?
a)
Growth
b)
Decay
36.
If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.
a)
1.25mg
b)
1.25g
c)
10g
d)
10mg
37.
If the half-life of uranium-232 is 70 years, how many half-lives will it take for 10 g of it to be reduced to 1.25 g?
a)
1 half-life
b)
2 half-lives
c)
3 half-lives
d)
4 half-lives
38.
If f(x) = 2x-9, what is f(3)?
a)
6
b)
-3
c)
3
d)
-6
39.
In an exponential function, what does the 'a' represent?
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
40.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
41.
James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.
a)
70(2)35
b)
70(2)5
c)
2(70)5
d)
5(70)2
42.
The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?
a)
9766
b)
9006
c)
9765
d)
5433
43.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1+14)x
c)
y=6(1.14)x
d)
y=6(0.86)x
44.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
45.
What is a, the starting term, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
46.
What is b, the common ratio, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
47.
What is a, the starting term, for the function: f(x) = 800(0.85)x?
a)
800
b)
0.85
c)
0.15
d)
x
48.
A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?
a)
y=78(0.5)x
b)
y=78(1.5)x
c)
y=78(2)x
49.
A 78 gram sample of Uranium loses half of its mass each year. How much is left after 6 years?
a)
13 grams
b)
6.5 grams
c)
1.22 grams
d)
592.31 grams
50.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
51.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
52.
The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?
a)
356
b)
265
c)
5825
d)
1329
53.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
54.
A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?
a)
14327
b)
4309
c)
839
d)
7680
55.
Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)x, where x is the number of years since January 1980. What is the percentage increase of the population annually?
a)
720,500%
b)
102.2%
c)
2.2%
d)
22%
56.
Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?
a)
102.2 people
b)
720,500 people
c)
1.022 people
d)
1022 people
57.
A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your growth rate, b?
a)
-5
b)
-.05
c)
.95
d)
.05
58.
A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. Approximately what would the population be after a year and a half?
a)
5295 beetles
b)
8.38E-21 beetles
c)
874 beetles
d)
2037 beetles
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