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Course: Algebra 2 > Unit 8
Lesson 3: The change of base formula for logarithms- Evaluating logarithms: change of base rule
- Logarithm change of base rule intro
- Evaluate logarithms: change of base rule
- Using the logarithm change of base rule
- Use the logarithm change of base rule
- Proof of the logarithm change of base rule
- Logarithm properties review
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Logarithm properties review
Review the logarithm properties and how to apply them to solve problems.
What are the logarithm properties?
Product rule | ||
Quotient rule | ||
Power rule | ||
Change of base rule |
Want to learn more about logarithm properties? Check out this video.
Rewriting expressions with the properties
We can use the logarithm properties to rewrite logarithmic expressions in equivalent forms.
For example, we can use the product rule to rewrite as . Because the resulting expression is longer, we call this an expansion.
In another example, we can use the change of base rule to rewrite as . Because the resulting expression is shorter, we call this a compression.
Want to try more problems like this? Check out this exercise.
Evaluating logarithms with calculator
Calculators usually only calculate (which is log base ) and (which is log base ).
Suppose, for example, we want to evaluate . We can use the change of base rule to rewrite that logarithm as and then evaluate in the calculator:
Want to try more problems like this? Check out this exercise.
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