What are logarithms? and Where did they come from? Foundations of Math 12 February 2016

Lets start with a puzzle You don’t know what the word “logarithm” or the mathematical notation “log” means, yet.  That’s okay.  Relax.     All of these statements are true: log2(8) = 3 log2(32) = 5 log3(9) = 2 log3(81) = 4 log5(5) = 1 Please do NOT use a calculator. Look at them carefully and try to think about how they could all be true.

NOW, lets see if you can fill in some blanks …   … to make some more true statements. Remember - do NOT use a calculator. a.     log2(16) = ____ b.     log6(36) = ____ c.     log5(____) = 3 d.     log7(1) = _____ e.     log2(____) = -1 f.      log10 11000= ____ g.     log____(81) = 2 h.     log____(81) = 4 i.       log16(____) = 1/2 j.       log8(2) = _____

Def: a logarithm is ___ _________  Log2(32) = 5 Say it: ____________________________ What it means: ____________________ Log3(27) = 3 Say it: ____________________________ Last one logb(a) = x Say it: ____________________________ So, Log4(16) = ___________

Def: a logarithm is ___ _________  

Looking at the definition and the beginning puzzles, we can see logs and exponents are related  

How are logs and exponents related?    8 x 6 = 48 ------- 48 /6 = 8

Why would we want to use logs anyway?  

Would you want to multiply 3.786 x 5.419 by hand?  

 

Lets look at a couple of problems … these use exponents to be solved   Remember: (1) x2 * x3 = x2+3 = x5 (2) = x-2 = 1 x2

Solving problems using rulers …  

 

 

 

 

 

In 2012,  

 

Logs around us:  

Logs around us:  

References   SlideShare – K Nowak SlideShare – Rebecka Peterson