Logarithms and eBy: Cody Steiner

What Are Logarithms?● Logarithms use the abbreviation log to solve exponent problems such as

(10^x=100), and to change multiplication and division problems to subtraction and addition problems.

This would be solved using log by: x=log10(100) -10 is the base of log x=log100/log10 x=2

The Properties/Laws of log

-When dividing logs it is the same as subtraction, or, when subtracting logs it is the same as dividing. (law of quotient)log x/y= log x-log y or vise versa log x-log y=log x/y -When multiplying logs it is the same as adding, or, when adding logs it is the same as multiplying. (law of product)log x.y= log x+log y or vise versa log x+log y=log x.y -Equivalence Rulea^x=y = loga(y)=x -Power Ruleloga(x^y) = yloga(x)

Properties/Laws Continued-Base RuleLoga=1 The base is always 10 if not shown otherwise. -Log of 1log1=0

The History-Invented by John Napier, a Scotsman, and by Joost Burgi, a Swiss.-Napier's findings were published in 1614-Burgi's findings were published in 1620-Napier's approach was algebraic -Burgi's approach was geometric-Logs were developed to help simplify multiplication and division to adding and subtracting because there were no calculators available in this time period. (They are not needed so much now due to calculators)-Napier and Henry Briggs created the common system similars to today's system in 1624.-The real impact of the discovery was not discovered till later.

Use in the Classroom

-The main use in the classroom is to solve logarithmic equations and to understand how to use the entire system.

Use in the Real World-There are many, many, many uses for logarithms in the real world!! Here's a list:-FInancials such as the number of payments on a loan or how long it will take you to reach your payment-Measure ph-Large time lines or large distances -Decibel scales-Richter scales-Cryptography -Any growth or decay models -There are many other uses! Heres a couple articles on how logarithms are used in the real world.http://elonka.com/kryptos/mirrors/daw/steinarticle.html ttp://www.xpmath.com/careers/topicsresult.php?subjectID=4&topicID=5

What is "e"

-e is a constant equal to 2.71828....-e is the base of natural log (ln)-e is also known as Euler's number-The main use of e is to "undo" ln or natural log

Example of the Use of ee^x=80 ln(e^x)=ln80 x ln(e)=ln80 x=ln80 x=4.382...

Laws/Rules of "e"

-Since e is the base of ln then I will explain the laws of ln. -The laws of ln are simple... They are the same as the log rules!!!

The History of e

-Invented by Leonhard Euler, a swiss, in the 1720's-Was very important with the combination of the logarithms

Use in the Classroom

-The main use in the classroom of e is to solve natural log equations, used in growth and decay equations, and compound interest equations.

Uses of e in the Real World

-The two main uses of e in the real world are calculating continuous compounding problems, and displaying growth and decay models. -Some other uses include finding the curves of objects such as the Gateway Arch in St. Louis and finding probabilities.

Works Citedhttp://www.dummies.com/how-to/content/algebras-laws-of-logarithms.html

http://www.westcler.org/gh/outtda/pdf_files/History_of_Logarithms.pdf

http://answers.yahoo.com/question/index?qid=20080408170725AAPwQqK

http://elonka.com/kryptos/mirrors/daw/steinarticle.html

http://www.xpmath.com/careers/topicsresult.php?subjectID=4&topicID=5

http://mathforum.org/dr.math/faq/faq.e.html

http://www.ndt-ed.org/EducationResources/Math/Math-Geometry.htm

http://www.sosmath.com/algebra/logs/log4/log46/log46.html

And my math book