1. All About Logarithms Block 4 Jenna, Justin, Ronnie and Brian

2. All About Logarithms  Learning Objective: to learn everything there is to know and practice using logarithms.  Warm Up:  1)10³=  2)100000= 10 to the what power?

3. Background Info  John Napier (inventor of the logarithm)  Born in 1550  Did not enter school until the age of 13  Was greatly interested in astronomy  Was involved in astronomy research that involved long and complicated calculations  This lead to his discovery of logarithms  First known discovery of logs in 1614 in a book called A Description of the Wonderful Canon of Logarithms  Died in 1617

4. What is a logarithm?  A logarithm is the power of ten that gives you the product  Ex: 10³=1000  Logarithm of 1000 is 3  Can also write as log 1000=3 10

5. Log rules  1) log (mn) = log (m) + log (n)  2) log (m/n) = log (m) – log (n)  3) log (mn) = n · log (m)  http://www.youtube.com/watch?v=10lPgI cWaKg http://www.youtube.com/watch?v=10lPgI cWaKg http://www.youtube.com/watch?v=10lPgI cWaKg b b b b b b b b

6. Natural Log  A natural log is a log with an irrational number as the base  base e, = log x or ln x e

7. Log Tables  Were used before calculators as a way to multiply and divide large numbers.  Can take the number of zeroes and that is the log of that number  EX: 1000*100=10000  Add three zeroes and two zeroes=five zeroes!  125 would have two zeroes if it were 100.  So, it is a little more than 100  Log(125) is 2.09691

8. Evaluating Logs  http://www.youtube.com/watch?v=nxsPlx YbLJ4 http://www.youtube.com/watch?v=nxsPlx YbLJ4 http://www.youtube.com/watch?v=nxsPlx YbLJ4

9. Logarithmic equations  http://www.youtube.com/watch?v=arBR2 ErXkyA http://www.youtube.com/watch?v=arBR2 ErXkyA http://www.youtube.com/watch?v=arBR2 ErXkyA  http://www.youtube.com/watch?v=e5B5E JJGP4Q http://www.youtube.com/watch?v=e5B5E JJGP4Q http://www.youtube.com/watch?v=e5B5E JJGP4Q

10. Practice problems  1) Solve.  Do so by rewriting the equation in exponential form.

11. More Practice Problems  2) Solve  Do this by applying the function  This will give you  Now use your log rules to simplify the left side….

12. Closing  Out: None  Summary: Today, I learned about logarithms.

13. Citations  Napier, John. "Logarithms: Large Numbers Simplified". ask.com. 4/19/10 <http://math.about.com/library/weekly/blbionapier.htm <http://math.about.com/library/weekly/blbionapier.htm  Stapel, Elizabeth. "Basic Log Rules / Expanding Logarithmic Expressions." Purplemath. Available from http://www.purplemath.com/modules/logrules.htm. Accessed 19 April 2010 http://www.youtube.com/watch?v=nxsPlxYbLJ4 http://www.purplemath.com/modules/logrules.htm http://www.youtube.com/watch?v=nxsPlxYbLJ4http://www.purplemath.com/modules/logrules.htm http://www.youtube.com/watch?v=nxsPlxYbLJ4  http://www.youtube.com/watch?v=arBR2ErXkyA http://www.youtube.com/watch?v=arBR2ErXkyA  http://www.youtube.com/watch?v=e5B5EJJGP4Q http://www.youtube.com/watch?v=e5B5EJJGP4Q  http://www.youtube.com/watch?v=10lPgIcWaKg http://www.youtube.com/watch?v=10lPgIcWaKg  "Logarithms Explained". Zyra.org. 4/19/10..