Monday, June 1, 2009

Exponents and Logs


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

An exponent

(log to the base a of x)

Properties of logs

Log base e (ln)


Change of Base Formula

Exponential Function
The inverse of y= is y=x

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.)



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

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

10) x = 9


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.