8.1.notebook
April 30, 2015
8.1 Understanding Logarithms
A logarithm is an exponent. Logarithms are simply another way to arrange information involving bases and exponents.
Example: Evaluate
This expression is read as "log base 5 of 25", which means "what exponent on 5 will give us a result of 25?" Of course, the answer is 2 (5 2 = 25).
Therefore, Log5 25 = 2
A logarithm is an exponent
Sep 27­8:42 AM
Example 1
Logarithmic Form
log39 = 2
Exponential Form
32 = 9
These two expressions are equivalent. They are simply different ways to express the same information. Remember ­ a logarithm is an exponent.
Example 2
Exponential Form
24 = 16
Logarithmic Form
log216 = 4
Sep 29­8:48 PM
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8.1.notebook
April 30, 2015
Convert from exponential form to logarithmic form.
Exponential Form
Logarithmic Form
1. 24 = 16
1.
2. 45 = 1024
2.
3. 73 = 343
3.
4. 62 = 36
4.
5. 53 = 125
5.
Sep 27­8:43 AM
Convert from logarithmic form to exponential form.
Logarithmic Form
Exponential Form
1. log3 9 = 2
1.
2. log2 32 = 5
2.
3. log4 64 = 3
3.
4. log5 25 = 2
4.
5. log7 49 = 2
5.
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8.1.notebook
April 30, 2015
Evaluating Logarithmic Equations
First change the equation into an exponential equation. Then solve the exponential equation.
Example: Solve for x: Log2 x = 3
Change to an exponential equation 23 = x
Now, solve for x: 23 = 8
Therefore x = 8
Sep 27­8:44 AM
Evaluate the following logarithmic equations and expressions
log5 125
log2 32
log3 x = 4
log7 x = 2
log7 x = 0
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8.1.notebook
April 30, 2015
Evaluate each of the following:
c) b)
a)
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Solve for x:
a)
b)
c)
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8.1.notebook
April 30, 2015
Graph y = 2x and its inverse.
a) Domain and Range of the inverse?
D: R: b) x and y intercepts of inverse?
c) Equation of the asymptote of the inverse?
d) What is the equation of the inverse?
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Homefun
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