# 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:

log_{b}(*MN*)=log_{b}(*M*)+log_{b}(*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:

log_{b}(*M/N*)=log_{b}(*M*)−log_{b}(*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:

log_{b}(*M ^{n}*)=

*n*log

_{b}(

*M*)