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Logarithms

Root  Derivative,  Indefinite integral,   Definite integral.....This stuff is important.  I put it here for the same reason there is a picture of Kim Jong-Il in every room in North Korea-- So it will stay in the front of the mind.

(Keep with me, there is a point in here)

As humans we think in very linear terms, like squirrels or lemmings (gerbils??)......The heuristics driving us to collect one nut after another, or following the herd, (or whatever it is that gerbils have done to gain such notoriety) make us commonly misinterpret reality and to act irrationally.  I don't think that it is too strong of a statement to say:  "If everyone in the world had a better understanding of the calculus, world peace follow."  Or at least we would not eat as many nuts or talk about gerbils.....

Just think if the squirrel could postulate 

 "Gee, if I saved some nuts till spring, and spent less time chasing Mrs. Squirrel to plant them and tend to them, and convinced other squirrels to help me, then after years, the growth of my wealth in terms of nuts, trees, land, and lady squirrels (Wn,t,l,ls)    could be described as a power function of e, of the form  f(x) = kxsince   \displaystyle{growth = e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n},  dang that makes a lot of sense, so I'm not going to worry about that pesky gerbil in the next tree that keeps wanting to crawl in my hole and take my nuts and pet Mrs. Squirrel.  Let him keep thinking about his marginal benefit of one more nut and one more session with Mrs. Squirrel....heck that's all small stuff, no sweat....I've got my eye way out on the horizon....See Squirrel Peace......errr....World Peace I mean.....depends on the scale of your tree I suppose.

Anyway.....
They understood it a long time ago, so why don't they teach relativism in grammar skool?  Then Calculus in middle skool, Linear Algebra in high skool, and keep the college kids busy with hydroponics and the humanities?

  See how well it works when you think about it all the time?      
   Just one slip and you're: 


So remember......

log(x)

Root
x = 1

Derivative
d/dx(log(x)) = 1/x

Indefinite integral
integral log(x) dx = x log(x)-x+constant

Global minimum
min {log(x)} = -infinity at x = 0

Definite integral
integral_0^1log(x) dx = -1