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Mathorio

Worksheet

Definition of a Logarithm

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Show your work for each problem.

1.
What does mean in exponential form?
1. a)
2. b)
3. c)
4. d)
2.
Evaluate .
3.
In the expression , what is the base?
1. a)125
2. b)5
3. c)3
4. d)25
4.
Evaluate .
5.
Write in logarithmic form.
6.
Evaluate (common logarithm).
7.
What is for any valid base ?
1. a)
2. b)0
3. c)1
4. d)undefined
8.
Evaluate .
9.
Evaluate .
10.
What is for any valid base ?
1. a)1
2. b)0
3. c)
4. d)
11.
Write in exponential form.
12.
Evaluate .
13.
Which of the following is NOT a valid logarithm?
1. a)
2. b)
3. c)
4. d)
14.
If , find the value of .
15.
Evaluate .
16.
Why is undefined?
1. a)5 is not a perfect power
2. b)Logarithms only work with base 10
3. c) for all , never 5
4. d)The base must be greater than 5