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Wednesday, May 24, 2006

May 24th Scribe By Marcquin

Well lets see here... Todays first class in morning we began with some questions.

Write as an expontial
a) log264 = 6
64 = 26

b) log7 343 = 3
343 = 73

Write as a logarithm
a) 38 = 6561
log36561 = 8

b) 253/2 = 125
log25125 = 3/2

Evaluate:
a) log243/2
log2(22)3/2
log223

b) 5log510 = 10



Solve:

logt4 = 2
22 = t2
2 = t


Expand

log2 (m3 n5)1/2 = 3/2 log2m+ 5/2 log2n
bring down the 1/2, therefore

1/2 log2 (m3 n5)

Remember "power of a power"

log2 (m3/2 n5/2)
multiply the exponents
log2m3/2 + log2n5/2


Given: log5 = 0.70 log2 = 0.30
without using a calculator find log 0.08

Start of by saying 0.08 = 8/100
If you look at the number it can be simplified to 2/25

You must use a power to get a power which will get you 2/ 52

Answer: log 0.08 = log (2/52)

0.08 = log 2/52
= log 2 - 2 log5
= 0.30 - 2 (0.70)
= 0.30 - 1.40
= - 1.10

Solve: logax + loga(x-2) = loga3

logax(x-2) = loga3
x2-2x = 3
x2-2x-3 = 0
(x-3) (x+1) = 0
x=3 Accept
x=-1 Reject

We also had a talk about the population question in class. I am sorry guys because I lost the notes for it.


Journal Notes

EXPONENTS AND LOGARITHMS

Exponential Function: Any function where the variable is an exponent written in the form




f(x) = ab
THE ROLE OF PARAMETER A
a determines the y-intercept of the function a.k.a. the initial value (i.e. x=0) of the function.
a<0>the graph is reflected in the y-axis
THE ROLE OF PARAMETER B
b is the base of the exponential function
b is also known as the multiplication factor.
b>1 the function is increasing. This is known as "exponential growth".
0the function is decreasing. This is known as "exponential decay".
LOGARITHMS
Definition: 1) A logarithm is a function that turns a power into an exponent.
2) The logarithmic function, logba = c, is the inverse of the exponential function bc = a where b does not equal zero and a>0.
logb a = c
b is the base
a is the argument
c is the logarithm
which means
bc = a
b is the base
a is the power
c is the exponent
Examples: log381 = 4 means 34 = 81
log232 = 5 means 25 = 32
log4 (1/16) = -2 means 4-2 = 1/16
log51/125 = -3 means 5-3 = 1/125
log100 = 2 means 102 = 100

GRAPHICALLY
Since the logarithm function is the inverse of the exponential function...






Remember: A logarithm is an exponent!






LAWS OF LOGARITHMS
Product law: logamn = logam + logan
Example: log2(4 * 32) = log24 + log232

Quotient law: loga(m/n) = logam - logan
Example: log3(81/27) = log381 - log327

Power law: logamb = b logam
Example: log5253 = 3 log525

Change of base law: logam = logbm all over log ba
Example: log84 = log24 all over log28


SPECIAL CASES:

1) logaa = 1
2) loga1 = 0
3) logaax = x
4) alog a x = x

The Common Logarithm
A logarithm function to the base 10 ( log10x) is called a "common logarithm". This base is so frequently used that it is simply written as log x, without the base indicated.
When no base is indicated, base 10 is assumed.

THE NATURAL LOGARITHM

e = 2.718281828459...

e is a number that arises naturally in the study of exponential functions, particularly in the case of continuous exponential growth. The natural logarithm function is written as:

lnx i.e. logex = lnx

read as "el-en of x"

And thats the whole bottle of wax for today!

So I will end off with a joke, haha just joking guys. So the next scribe has to be jan. It was inevitable!



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2 Comments:

At 5/25/2006 7:24 AM, Blogger Mr. H said...

Nice Scribe Post. You are continuting the excellent scribbing going on in this class. Your choice of font for your definitions could be larger. I am having a hard time reading it. If you change your font this would be ready for the Hall of Fame.

Mr. Harbeck
Sargent Park School

 
At 5/31/2006 9:14 AM, Blogger Mr. Kuropatwa said...

This is an outstanding scribe post Marquin! Take Mr. H's advice and then we can induct you into the Scribe Post Hall of Fame!

 

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