Logarithms

Site: | TBAISD Moodle |

Course: | Michigan Algebra II Preview 2012 |

Book: | Logarithms |

Printed by: | Guest user |

Date: | Friday, July 30, 2021, 07:34 PM |

Method 1

There are many different types of logarithmic equations. The first type uses properties to convert more than one log into a single log expression and then applies inverses to solve.

**Example** 1 Solve log_{3} 4 + log_{3} x = 1

*Step 1. *Use properties to convert to a single log.

*Step 2. *Translate the log equation to its equivalent exponential form.

*Step 3. *Solve for *x*.

Example 2

Solve the equation log _{4}3 - log _{4}12 = x

*Step 2. *Translate the log equation to its equivalent exponential form.

*Step 3. *If needed, change the two expressions to the same base and solve for *x*.

Method 2

Another type of log equation is one where there is a log on both sides of the equal sign. To solve this type of equation, use the inverse relationship between logs and exponents.

**Example 1** Solve the equation

Step 1.UseProduct of a Power Propertyto convert to a single log.

Step 2.Use the inverse operation of exponents on both sides of the equals sign. Since the log has a base of 2, use an exponential base of 2.

Step 3.Since logs and exponents are inverses, the exponent base and the log base cancel.

Step 4. Solve forx.

* *

Example 2

Solve the equation

Step 1.UsePower of a Power Propertyto convert to a single log.

Step 2.Use the inverse operation of exponents on both sides of the equals sign. Since the common log has a base of 10, use an exponential base of 10.

Step 3.Since logs and exponents are inverses, the exponent base and the log base cancel.

* *

Step 4. Solve forx.

* *

Guided Practice

To solidify your understanding of evaluating exponential and logarithmic equations, visit the following link to Holt, Rinehart, and Winston Homework Help Online. It provides examples, video tutorials, and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Sources

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

Glencoe, McGraw-Hill, "Properties of Logs." http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-827999-2&chapter=10&lesson=3&headerFile=4&state=fl (accessed 7/13/2010).

Holt, Rinehart & Winston, "Solving Exponential and Logarithmic Equations." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch07_05_homeworkhelp.html (accessed 7/13/2010).

Holt, Rinehart & Winston, "Solving Logarithmic Equations." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=7152/7152.xml (accessed 7/13/2010).