Section 4.5 - Exponential and Logarithmic Equations

Section Objectives

  1. Solve exponential equations.
  2. Solve logarithmic equations.
  3. Use and solve exponential and logarithmic equations in applications.



Two Important Properties for Solving Equations

Some kinds of logarithmic and exponential equations can be solved by appealing to the one-to-one property of logarithms and exponentials:



In order to use these properties, (1) the equation must be written with a single term on each side of the equation, and (2) each side must have an expression in the same base.



Examples










Other equations can be solved by using the properties of logarithms and exponentials. The following examples are typical.