Properties of Logarithms
Our relationship is
We want to use logarithms to convert this to a line (because we know how to fit a line!). First, it may be helpful to review some properties of logarithms.
Logarithm Properties
The three major logarithm properties we use are the following product, quotient, and power rules. For a more in depth review, visit this chapter of OpenStax College Algebra on Logarithmic Properties.
THE PRODUCT RULE FOR LOGARITHMS
The product rule for logarithms can be used to simplify a logarithm of a product by rewriting it as a sum of individual logarithms:
logb(MN)=logb(M)+logb(N) for b>0
THE QUOTIENT RULE FOR LOGARITHMS
The quotient rule for logarithms can be used to simplify a logarithm or a quotient by rewriting it as the difference of individual logarithms:
logb(M/N)=logb(M)−logb(N)
THE POWER RULE FOR LOGARITHMS
The power rule for logarithms can be used to simplify the logarithm of a power by rewriting it as the product of the exponent times the logarithm of the base:
logb(Mn)=nlogb(M)