Exponentials

Exponentials

Site: | TBAISD Moodle |

Course: | Michigan Algebra II Preview 2012 |

Book: | Exponentials |

Printed by: | Guest user |

Date: | Friday, January 15, 2021, 10:42 PM |

Method 1

There are two methods for solving exponential equations. The first method requires that the bases in both exponentials are the same. If the two sides of the original equation do not have the same base, it is sometimes possible to rewrite them with the same base. This method uses an exponential property which states:If then .

**Example 1 ** Solve

Example 2

SolveMethod 2

The second method for solving exponential equations involves using logarithms. For example, when trying to solve 3^{x} = 11, 3 and 11 cannot be written as like bases. The log of both sides will need to be determined.

**Example 1** Solve the equation

In this example, common logs were used but any base can be used.

Example 2

Solve

*Step 2. *Since there is no common base, apply logarithms.

*Step 3. *Use the *Power to a Power Property.*

*Step 4. *Solve for *x*.

*Step 5. *Use a calculator to find the answer.

*Step 6. *Check the answer.

Video Lesson

To learn how to solve exponential equations, select the following link:Solving Exponential Equations

Sources

Sources used in this book:Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart, & Winston, "Solving Exponential Equations." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=6465/6465.xml (accessed 7/13/2010).