Wednesday, February 14, 2007

7-5 : Logarithimic Functions!!!

Hey folks...I am here...to teach you...all about...LOGARITHIMIC FUNCTIONSSS CUZ IM RICK JAMES silly goose. So...let's get started


We all know that a logarythm is the inverse of an eponential function. Therefore we can deduce (big word) that if given a set of data, and it is a logarhythm, then it will follow the multiply - add pattern. Observe...

x y

6 1
18 2
54 3
162 4
486 5
1358 6

the x-values are multiplied by a factor of 3, every time the y-values add 1.


Recap of what a log function is :
y =a + b log x
a graph of this would look like this (notice that it contains the point (1,0))

























Ok now a little bit more algebra stuff for all of you guys...*using the formula, y = a + b ln(x)*

1 = a + b ln(6)

2 = a + b ln(18)

subtract

-1 = b ln(6) - b ln(18)

take out b

-1 = b[ ln(6) - ln(18) ]

use quotient property

-1 = b[ ln(1/3) ]

divide both sides by ln(1/3)

b = -1/ln(1/3)

b = .910

ok now we solved for b, next is a

1 = a + .910 * ln(6)

isolate a

a = 1 - .910 * ln(6)

a = -.631

the answer is *drumroll please*

y = -.631 + .910 * ln(x)





Ok now I get the pleasure of showing you how to translate and dilate logarythms!!
in red is y = ln(x)
in blue is y = 2ln(x-1).........(notice that its asymptote is moved over to x=1, and that it does not taper off as quickly)






























Anything in the parenthesis with the x, affects the graph horizonatally, anything outside affects the graph vertically, just like always.





now this is a special case...this is the graph of log (x squared - 1)
the grey lines represent asymptotes, the red lines cross the x-axis at (-2, 0) and (2, 0)




























My Problem

the starting logarhythm function is y = 5 + ln(2x), increase the horizontal dilation by a factor of 2 and the vertical dilation by a factor 9.

answer : y = 5 + 9 * ln(x)


OK that is lesson 7-5 in a nutshell
reminder to P-dubs (paul)
www.themathpage.com/aPreCalc/logarithms.htm
and here is my personalization...
ok this is from arrested development the BEST show ever to air...and probably ever will air

Gob : hey, guy, They tell me you're the actor who plays Marta's brother, Tio
Spanish guy : Como?
Gob : Oh, you're gonna be in a coma alright...

:-D I love that show
ok goodnight everyone

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