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

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?

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

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

Log rules  1) log (mn) = log (m) + log (n)  2) log (m/n) = log (m) – log (n)  3) log (mn) = n · log (m)  cWaKg cWaKg cWaKg b b b b b b b b

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

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

Evaluating Logs  YbLJ4 YbLJ4 YbLJ4

Logarithmic equations  ErXkyA ErXkyA ErXkyA  JJGP4Q JJGP4Q JJGP4Q

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

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….

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

Citations  Napier, John. "Logarithms: Large Numbers Simplified". ask.com. 4/19/10 < <  Stapel, Elizabeth. "Basic Log Rules / Expanding Logarithmic Expressions." Purplemath. Available from Accessed 19 April     "Logarithms Explained". Zyra.org. 4/19/10..