7.3 Properties of logarithms
Unit 7 · Exponential and logarithmic functions
Ideas in this lesson
Product and quotient rules
A product becomes a sum of logarithms; a quotient becomes a difference. Every original argument must be positive.
Quotient rule
A quotient of positive arguments becomes the difference of their logarithms.
Power rule
An exponent in a positive logarithm argument can become a coefficient.
Expand and condense
Use the product, quotient and power rules in either direction while retaining the original domain.
Change of base
Divide logarithms of argument and base taken in the same valid new base.
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