WorksheetsLogarithmic & Exponential Review
Total questions: 45
Worksheet time: 2hrs 59mins
Name
Class
Date
1.
Use your calculator to approximate the log.
a)
A
b)
B
c)
C
d)
D
2.
Use your calculator to approximate the log.
a)
A
b)
B
c)
C
d)
D
3.
Rewrite in exponential form.
a)
A
b)
B
c)
C
d)
D
4.
Rewrite in exponential form.
a)
A
b)
B
c)
C
d)
D
5.
Rewrite the equation in logarithmic form.
a)
A
b)
B
c)
C
d)
D
6.
Rewrite the equation in logarithmic form.
a)
A
b)
B
c)
C
d)
D
7.
Expand the logarithm.
a)
A
b)
B
c)
C
d)
D
8.
Expand the logarithm.
a)
A
b)
B
c)
C
d)
D
9.
Expand the logarithm.
a)
A
b)
B
c)
C
d)
D
10.
Expand the logarithm.
a)
A
b)
B
c)
C
d)
D
11.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
12.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
13.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
14.
Condense into a single logarithm.
a)
A
b)
B
c)
C
d)
D
15.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
16.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
17.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
18.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
19.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
20.
Solve the equation.
a)
A
b)
B
c)
C
d)
D
21.
log525 = ?
a)
2
b)
5
c)
125
22.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
23.
Write as a single log: log 12 + 2 log x
a)
log (12 + 2x)
b)
log (14x)
c)
log (24x)
d)
log (12x2)
24.
Rewrite logb(xn)
a)
nlogbx
b)
(logbx)n
c)
xnlogbx
d)
logb(xn)
25.
Evaluate logb(b)
a)
-1
b)
0
c)
1
d)
b
26.
Simplify the expression
log(30)-log(6)
log(30)-log(6)
a)
-6log(30)
b)
log(24)
c)
log(-24)
d)
log(5)
27.
Rewrite as two logarithms.
a)
A
b)
B
c)
C
d)
D
28.
ln(eW)
a)
e
b)
W
c)
eW
d)
undefined
29.
log(10R)
a)
10
b)
1
c)
R
d)
10R
30.
10log(k)=
a)
k
b)
10
c)
10k
d)
1
31.
eln(f)
a)
f
b)
e
c)
ef
d)
undefined
32.
Describe the transformation of y=ln(x) that would give the graph for y = ln(x+7)
a)
vertical translation 7 up
b)
vertical translation 7 down
vertical stretch by a factor of 7
vertical stretch by a factor of 7
c)
horizontal translation 7 left
d)
horizontal translation 7 right
33.
Describe the transformation of y=ln(x) that would give the graph for y = 7ln(x)
a)
vertical translation 7 up
b)
vertical stretch by a factor of 7
c)
vertical compression by a factor of 7
d)
horizontal translation 7 left
34.
Describe the transformation of y=ln(x) that would give the graph for y = ln(-x)
a)
reflection over the line y=x
b)
reflection over the x-axis
c)
reflection over the y-axis
d)
reflection over the line y=-1
35.
52x=37
a)
x=1.568
b)
x=3.135
c)
x=1.122
d)
x=2.244
36.
What is the domain of y = log x
a)
[0,infinity)
b)
(0,infinity)
c)
(-infinity, infinity)
d)
(-infinity,0)
37.
What is the range of y = log x
a)
(-infinity,0)
b)
[0,infinity)
c)
(0,infinity)
d)
(-infinity,infinity)
38.
Evaluate the log:
log3(1/9) =
log3(1/9) =
a)
1/2
b)
2
c)
-2
d)
3
39.
Condense
no calculator
no calculator
a)
A
b)
B
c)
C
d)
D
40.
Expand
no calculator
no calculator
a)
A
b)
B
c)
C
d)
D
41.
Condense
no calculator
no calculator
a)
A
b)
B
c)
C
d)
D
42.
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
43.
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
44.
The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?
a)
100.0g
b)
50.0g
c)
12.5g
d)
8.5g
45.
If allowed to grow forever, a sunflower will have continuous exponential growth. Sunflowers grow at a rate of 0.8% per day. If a sunflower starts out at 2 inches, how long will it take to reach 3 feet?
a)
≈37 days
b)
≈6 days
c)
≈4 days
d)
≈1 days
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