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Definition: The inverse of is .
is called the logarithm of .
It is written as
It is read as "y equals log base b of x"
7.2 - 7.3 Logarithms
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Example 1: Write each equation in exponential form.
a. b.
c. d.
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Example 2: Write each equation in logarithmic form.
a. b.
c. d.
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Evaluating LogsExample 3: Evaluate each expression.
a. b.
c. d.
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*Note: For a logarithm that has no written base, the assumed base is 10.For example, in the expression , the base is 10.
Now evaluate
Use your calculator to evaluate
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Inverse Properties of Logs
and
One example of each property is below:
and
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Putting it all together!Evaluate the following:
a. b. c.
d. e. f.
g. h. i.
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Solving Logarithmic EquationsExample 4: Solve each equation.
a. b.
c. d.
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The Significance of ParenthesesCompare the following by solving:
vs.
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Solving Exponential Equations using Logarithms
Example 5: Solve each equation.
a. b.
c.d.
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Example 6: Graph the given function. State the domain and range. List any asymptotes and intercepts.
a.
Domain: Range:
Asymptote:
Graphing Logarithmic Functions
x-intercept: y-intercept:
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b.
Domain: Range: Asymptote:
x-intercept: y-intercept:
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Example 7: What are the x-intercepts and y-intercepts of the following graphs? Also, state the asymptote.
a. b.
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c.
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d.
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SOL Question - Multiple Choice