9.4 Properties of Logarithms
Remember:
Write in exponential form: log 3 = 0.477
Write in exponential form: ln 4225 = 8.35
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Explore - Adding Logs
1. Use your calculator to evaluate: log 100 + log 10
2. What type of number is your answer to #1?
3. Why does log 100 = 2? Why does log 10 = 1? Write each equation in
exponential form.
4. Use your answer to #1 and 3 how could you rewrite log 100 + log 10 in
exponential form?
5. How does 100 and 10 relate to your answer in #4?
6. Write a rule for adding logs with like bases.
7. Why do you think this rule works?
2
Explore - Subtracting Logs
1. Use your calculator to evaluate: log 1000 - log 10
2. What type of number is your answer to #1?
3. Why does log 1000 = 3? Why does log 10 = 1? Write each equation in
exponential form.
4. Use your answer to #1 and 3 how could you rewrite log 1000 - log 10 in
exponential form?
5. How does 1000 and 10 relate to your answer in #4?
6. Write a rule for subtracting logs with like bases.
7. Why do you think this rule works?
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Explore - Coefficients of Logs
1. Use your rule from adding logs to rewrite: log 2 + log 2 + log 2.
2. Use the idea of adding/subtracting like terms to rewrite log 2 + log 2 + log 2 in
another way.
3. Set your answers to #1 & #2 equal to each other. How do your answers relate
to each other?
4. Write a rule for coefficients of logs with like bases.
5. Why do you think this rule works?
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Properties of Logarithms
Expanded form
Condensed form
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Example 1: Express each logarithm in expanded form.
a)
b)
6
Example 2: Express in condensed form.
a)
b)
7
Example 3: Determine the domain of the logarithmic equation.
Then solve by expressing the equation in equivalent exponential form.
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