Section 5.3 Properties of Logarithms

Section Objectives

  1. Apply the logarithm laws.
  2. Use the logarithm laws to expand logarithmic expressions.
  3. Use the logarithm laws to expand logarithmic expressions.
  4. Apply the change-of-base formula.



Logarithm Laws

The following properties of logarithms are very useful.




Warning: Do not apply the logarithm laws when they do not apply. For example,



Examples
















Change-of-Base Formula

For any valid bases and and any positive real number ,



The change of base-of-base formula can be used to convert any log to a common or natural log.