Monday, June 1, 2009

Exponents and Logs

Exponents

Definitio
n: If n is a positive integer an x is a numerical base, then

(n times)

Exponential Rules




Radicals as Exponents











Exponential Functions

  1. Standard form of an exponential function is f(x)= a , where b>0, b1 and a is the y intercept.

Red - When x is a negative exponent

Blue - When x is a positive exponent

2. Shifting the Graph:

g(x) = f(x-2) shift 2 right

h(x) = f(x) - 2 shift 2 down

j(x) = -f(x) reflection in the x axis



Radioactive Decay

t = time, m = initial mass, h = half life

Natural Base e
  • e is a irrational number and is derived from computation:

  • e can be approximated using the following expression:


  • To imput into your calcuter, hit 2nd LN


Compounding Countinuously



Logarithm-
An exponent


(log to the base a of x)

Properties of logs




Log base e (ln)

a=ln(a)


Change of Base Formula



Exponential Function
The inverse of y= is y=x

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Example Questions:
Unless other directions are given, solve for x:




  1. Expand as a function of individual logs.


  2. Graph


  3. Given, for what value of t will P be greater than 200,000? (round to the thousandth.)


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Answers
1)

2) x = 119.89
3) x = 2.
77
4) x = 1.54
5)
3 ln(x) - (2 ln(y) +5 ln(z))
6) x = 7
7)

8) x = -1, x = 5
9) t = 24.26

10) x = 9

2 comments:

Kate Nowak said...

Good start!

I like how you were able to include some screenshots of pdf's downloaded from Blackboard. Very resourceful.

You need to remove some whitespace from your post!

Kate Nowak said...

Your "properties of logs" section is a bit hard to read, and could use some better spacing.

I also think you should include the log laws, for example log(ab) = log a + log b.