3.4 Solving Exponential and Logarithmic Equations

Introduction

There are two basic strategies you can use to solve these equations.

One-to-One Properties

 if and only if x=y

 if and only if x=y

Inverse properties

Examples of Exponential Equations:

Can be we written as:

By the one-to-one property, x=5

x=ln 7 by the Inverse property

Solving an Exponential Equation in Quadratic Form

   or   

          

          

                     x  =  0

Solving Logarithmic Equations

ln x = 2

Exponentiate each side

Final Answer Without a Calculator

Solving a Logarithmic Equation

Isolate the log (divide both sides by 2)

Exponentiate both side (by base 5)

Use the inverse property

Change-of-Base Formula