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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