Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.4
Page 1 / 4
Logarithms
Goal: Be able to convert a function from exponential form to logarithmic form
First, identify whether this equation is in exponential or logarithmic form, then convert it into which
form it’s not written in. If the given equation is (or can be written as) a logarithm that has a specific
name (common log, etc), write that down, too.
1)
23  8
2)
log 4 16  y
3)
log 270  y
4)
103  1000
5)
ln 30  x
6)
log e 270  y
8)
log 1
7)
32

1
5
1

2
e
Logarithms – Exact Answers
Goal: For each of the following problems, find an exact solution for x
9)
log 2 64  x
10)
log 10 100  x
11)
log 10
12)
log 4
13)
log x 9  2
1
x
100
1
x
64
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45
y
7
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.4
Page 2 / 4
Logarithms – Domain
Goal: For each of the following find the domain of the function:
14)
15)
16)
17)
f  x   log 4
x
7
x2
f x   log 4
7
2
f x   log 4 x  1
 7 
f  x   log 4 

x

2




 2 

18) f  x   log 4 
x 3


2

X
Logarithms – Graphing
Goal: Graph (by hand) the following transformations of the logarithmic / exponential functions
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
19)
2 3 4 5 6 7 8 9 10
Y
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f x   log 7 x  2  1
X
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
§ 4.4
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20)
f x   log x  2  1
21)
f x   log 1 x  2  1
2 3 4 5 6 7 8 9 10
X
Y
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
2
2 3 4 5 6 7 8 9 10
Y
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 4.4
Page 4 / 4
Logarithms – Solving them
Goal: Be able to manipulate equations with simple logarithms in them, so that you can solve them.
22) Solve for x:
log x 64  2
23) Solve for x:
ln e x  5
24) Solve for x:
log 5 x  3
25) Solve for x:
log x 27  3
26) Solve for x:
e2 x 5  8
27) Solve for x:
10 2 x  7  4
28) Solve for x:
log 3 x  2
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