Math 1314
Logarithms
Vocabulary:
Section 4.2 Notes
logax = y is called the logarithmic form.
ay = x is called the exponential form.
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Math 1314
Examples: Write each expression in exponential form.
Section 4.2 Notes
1. log6 1= 0
1
2. log 2    3
8
3. log 1000 = 3
4. log25 5 = ½
2
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Math 1314
Examples: Write each expression in logarithmic form.
Section 4.2 Notes
1. 24 = 16
2. 53 = 125
3
1
1
3.   
8
2
4. 2-5 = 0.03125
Evaluating Logarithms
For a > 0 and a ≠ 1, logax = y if and only if ay = x
Thus, logax is the exponent in which the base a must be raised to give x.
Memorize: The logarithm y of a real number x ( x> 0) is the exponent to which the base a (a > 0, a ≠ 1)
must be raised to yield that number x.
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Math 1314
Section 4.2 Notes
Examples: Evaluate each expression.
1. log327
2. log749
3. log 2
1
8
4. log6
1
6
5. log164
4
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Math 1314
Section 4.2 Notes
6. log5 5
7. log 3
1
3
8. log121
5
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Math 1314
Section 4.2 Notes
IMPORTANT:
You cannot apply a logarithm to zero or to a negative number !!!
Examples:
Simplify each of the following:
1. log 3 9 
2. log 2
1

4
6
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Math 1314
Section 4.2 Notes
3. log 5 5 
4. log 4 64 
5. log2 (4) 
6. log 5 0 
7. log11 11
8. 5log5 7
7
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