All About All About LogarithmsLogarithmsBlock 4Block 4

Jenna, Justin, Ronnie and BrianJenna, Justin, Ronnie and Brian

All About LogarithmsAll About Logarithms

Learning Objective: to learn everything Learning Objective: to learn everything there is to know and practice using there is to know and practice using logarithms.logarithms.

Warm Up: Warm Up: 1)10³=1)10³= 2)100000= 10 to the what power?2)100000= 10 to the what power?

Background InfoBackground Info

John Napier (inventor of the logarithm)John Napier (inventor of the logarithm) Born in 1550Born in 1550 Did not enter school until the age of 13Did not enter school until the age of 13 Was greatly interested in astronomy Was greatly interested in astronomy Was involved in astronomy research that involved Was involved in astronomy research that involved

long and complicated calculationslong and complicated calculations This lead to his discovery of logarithmsThis lead to his discovery of logarithms

First known discovery of logs in 1614 in a book First known discovery of logs in 1614 in a book called called A Description of the Wonderful Canon of A Description of the Wonderful Canon of LogarithmsLogarithms

Died in 1617Died in 1617

What is a logarithm?What is a logarithm?

A logarithm is the power of ten that gives A logarithm is the power of ten that gives you the productyou the product Ex: 10Ex: 10³=1000 ³=1000 Logarithm of 1000 is 3Logarithm of 1000 is 3

Can also write as log 1000=3Can also write as log 1000=310

Log rulesLog rules

1) 1) log log ((mnmn) = ) = loglog ( (mm) + ) + loglog ( (nn)) 2) 2) log log ((mm//nn) = ) = loglog ( (mm) – ) – loglog ( (nn)) 3) 3) log log ((mnmn) = ) = nn · · loglog ( (mm))

http://www.youtube.com/watch?v=10lPgIcWaKg

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b

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b

b

b

b

b

Natural LogNatural Log

A natural log is a log with an irrational A natural log is a log with an irrational number as the basenumber as the base

base e, = log base e, = log xx or ln or ln xx e

Log TablesLog Tables

Were used before calculators as a way to Were used before calculators as a way to multiply and divide large numbers.multiply and divide large numbers.

Can take the number of zeroes and that is Can take the number of zeroes and that is the log of that numberthe log of that number EX: 1000*100=10000EX: 1000*100=10000

Add three zeroes and two zeroes=five zeroes!Add three zeroes and two zeroes=five zeroes!

125 would have two zeroes if it were 100.125 would have two zeroes if it were 100. So, it is a little more than 100So, it is a little more than 100

Log(125) is 2.09691Log(125) is 2.09691

Evaluating LogsEvaluating Logs

http://www.youtube.com/watch?v=nxsPlxYbLJ4

Logarithmic equationsLogarithmic equations

http://www.youtube.com/watch?v=arBR2ErXkyA

http://www.youtube.com/watch?v=e5B5EJJGP4Q

Practice problemsPractice problems

1) Solve. 1) Solve. Do so by rewriting the equation in Do so by rewriting the equation in

exponential form.exponential form.

3)43(log6 x

More Practice ProblemsMore Practice Problems

2) Solve 2) Solve Do this by applying the functionDo this by applying the function This will give youThis will give you Now use your log rules to simplify the left Now use your log rules to simplify the left

side…. side….

3)43(log6 x

xy 63)43(6log 66 x

ClosingClosing

Out: NoneOut: None

Summary: Today, I learned Summary: Today, I learned about logarithms.about logarithms.

CitationsCitations

Napier, John. "Logarithms: Large Numbers Simplified". Napier, John. "Logarithms: Large Numbers Simplified". ask.com. 4/19/10 ask.com. 4/19/10 <http://math.about.com/library/weekly/blbionapier.htm

Stapel, Elizabeth. "Basic Log Rules / Expanding Logarithmic Stapel, Elizabeth. "Basic Log Rules / Expanding Logarithmic Expressions." Expressions." PurplemathPurplemath. Available from. Available from        http://www.purplemath.com/modules/logrules.htmhttp://www.purplemath.com/modules/logrules.htm. . Accessed 19 April 2010Accessed 19 April 2010http://www.youtube.com/watch?v=nxsPlxYbLJ4http://www.youtube.com/watch?v=nxsPlxYbLJ4

http://www.youtube.com/watch?v=arBR2ErXkyAhttp://www.youtube.com/watch?v=arBR2ErXkyA http://www.youtube.com/watch?v=e5B5EJJGP4Qhttp://www.youtube.com/watch?v=e5B5EJJGP4Q http://www.youtube.com/watch?v=10lPgIcWaKghttp://www.youtube.com/watch?v=10lPgIcWaKg "Logarithms Explained". Zyra.org. 4/19/10 "Logarithms Explained". Zyra.org. 4/19/10

<http://www.zyra.org.uk/logs.htm>. <http://www.zyra.org.uk/logs.htm>.