# Properties of Logarithms

This material should be review, but is provided here for your reference.

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)