Key Terms & Glossary
Key Equations
The Product Rule for Logarithms | |
The Quotient Rule for Logarithms | |
The Power Rule for Logarithms | |
The Change-of-Base Formula |
Key Concepts
- We can use the product rule of logarithms to rewrite the log of a product as a sum of logarithms.
- We can use the quotient rule of logarithms to rewrite the log of a quotient as a difference of logarithms.
- We can use the power rule for logarithms to rewrite the log of a power as the product of the exponent and the log of its base.
- We can use the product rule, the quotient rule, and the power rule together to combine or expand a logarithm with a complex input.
- The rules of logarithms can also be used to condense sums, differences, and products with the same base as a single logarithm.
- We can convert a logarithm with any base to a quotient of logarithms with any other base using the change-of-base formula.
- The change-of-base formula is often used to rewrite a logarithm with a base other than 10 and e as the quotient of natural or common logs. That way a calculator can be used to evaluate.
Glossary
- change-of-base formula
- a formula for converting a logarithm with any base to a quotient of logarithms with any other base.
- power rule for logarithms
- a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base
- product rule for logarithms
- a rule of logarithms that states that the log of a product is equal to a sum of logarithms
- quotient rule for logarithms
- a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms