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

2. 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.

3. 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.      log = ____
g.     log____(81) = 2
h.     log____(81) = 4
i.       log16(____) = 1/2
j.       log8(2) = _____

4. 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) = ___________

5. Def: a logarithm is ___ _________

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

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

8. Why would we want to use logs anyway?

9. Would you want to multiply 3.786 x 5.419 by hand?

11. 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

12. Solving problems using rulers …

18. In 2012,

20. Logs around us:

21. Logs around us:

22. References
SlideShare – K Nowak
SlideShare – Rebecka Peterson