Reflection on Exponents and Logarithms

Um hi, I'm your alternate scribe for the day since Emmelion was not present in class. But this isn't the scribe post just yet, it's just my BOB because our test is tomorrow..

It feels to me as though this unit went by quickfast. The logs deal sounds simple enough, or not. XD It does get disconcerting every once in a while but I'll be fine.. I hope so anyway.

Er, we've ended the unit off with exponential modelling which is the hard part for me. I need to figure out which formula to implement for various cases. I guess it's time to whip out that exercise booklet we were given at the beginning of the course. 8)

Important things to remember:

The Anatomy of a Power:
a^b = c

a is the base.
b is the exponent.
c is the power.

Exponential Functions have asymptotes.

A logarithm is an exponent!!! (Just saying.)

log_ac = b

a is the base.
b is the exponent.
c is the power.

Given f(x) = log_dx...

In f(x):
Inputs are exponents.
Outputs are powers.

In f^-1(x):
Inputs are powers.
Outputs are exponents.

(log_ax is just the inverse of a^x.)

The Product Law:
log_bMN = log_bM + log_bN

The Quotient Law:
log_b = log_bM - log_bN

The Power Law:
log_bM^k = klog_bM

The Change of Base Law:

log_aa^x = x

The Common Logarithm: when no base is indicated, the base of the logarithm is 10

The Exponential Function
f(x) = e^x

The Natural Logarithm
f(x) = ln(x)

Formulas, ahhhh!

A = P(1+)^tn

A is the amount.
P is the principle.
r is the interest rate.
n is the times you compound.
t is the time.

A = Pe^rt
(with continuous interest? :S)

A = A₀(m)^t

A₀ is the original amount.
m is the multiplication factor or growth rate.

A = A₀(m)^t/p

p is the period; amount required to multiply by "m" once.

D: That took much longer than I expected. Hmm, I hope I got all the information right, else leave me a comment and I'll change it ASAP. :) Yeah, good luck to everyone on the test and you know.. study. Don't forget your delicious links too!