## Tuesday, May 5, 2009

### BOB on Exponents and Logarithms

Hey guys, please excuse this extremely out of place BOB-post! As some of you may know, I missed last week's test on Exponents and Logarithms and so my test is scheduled for tomorrow :].
I will try to make this BOB post substantial enough, but I don't know exactly how much I'm going to say so here I go!

Honestly, I think I'm going to find certain aspects of this unit test difficult! I've got the hang of everything we learned from the beginning of the unit up until the part when I left for the week. That means natural logarithms and the accounting portion will probably throw me off big time :/ Oh! And graphing logarithms... Ugh D: Nonetheless I will study hard!

Firstly, I must remember that a logarithm is an exponent! Don't forget!
This, as we all must know, is the basic form of an exponential equation:
On the other hand, the basic form of a logarithmic equation is:

In both cases;
a is the base
b is the exponent
c is the power

Now, there are several laws pertaining to logarithms. They are the Power, Product, Quotient, and Change of Base laws.
Power Law:Product Law:Quotient Law:Change of Base Law:
Ah, I almost forgot to mention that a logarithm is the inverse of an exponent! This comes in handy when dealing with graphing! We know that the exponential function results with the power when given an exponent. Therefore, a logarithmic function results in the exponent when given the base and power.

Alright, I can't quite say much about e other than I have noo idea what it is other than a "natural number" (?). I'm looking up websites and working on exercises as we speak! I will get the hang of thiiiis.

Also, we were given formulas pertaining to exponential/logarithmic growth and decay! Here they are, sadly though - they remind me a whole lot of Business class lol. Maybe that's a good, helpful thing?

PERT Formula:
Pe ^ rt = A
(for some weird reason the image maker won't allow me to have an exponent of rt :<)
P is the principle
e is the natural number
r is the rate
t is the amount of time
A is the total amount

MODEL Formula:

Ao is the original amount
m is the multiplying factor
t is the amount of time in total
p is the period of time it takes
A is the total amount

PERT's BROTHER Formula:
P(1+r/n) ^ tn = A
(again, some deal with the PERT formal, they really are brothers!)
P is the principle
1+r/n is the principle plus the rate over the number of times it is compounded a year (annually, biweekly, etc)
t is the amount of time

Okay! I think that's all about I
can say... Of to study some more~
Wish us luck guys ;D!