Section 5.3 - Logarithms!

This section was on logarithms! Logarithms are basically the inverse of an exponential equation. Literally, it means ratios of numbers.

exponentiation is what is being done to X in this case.


To solve, we need to undo what is being done to X, which is a logarithm :)

Mr. Wilhelm's KEY TO EVERYTHING!

That is how to rewrite an exponential function as a logarithmic function. With this, we can solve exponential equations that would otherwise be unsolvable!

This is how you might apply a logarithm to an exponential function. As you can see, Y=1,000  A=10   and X=3

The key to everything is as easy as that :)

Special Logarithms!

When it is just written "log" with no subscript, it is implied that it is log10 -- COMMON LOG!

When it is written ln, it is implied that it is loge -- NATURAL LOG!

How to graph a logarithm!

A few other little tidbits to know:

since the domain of an exponential function is (-∞, ∞), so thats the RANGE of a logarithm

the range of an exponent is (0, ∞), so thats the DOMAIN of a logarithm. (unless it has been moved by the C value)

*Exponents and Logarithms are 1 to 1*

Sorry, there are no pretty logarithm pictures on the internet :(

Links and stuff:

http://www.themathpage.com/aprecalc/logarithms.htm

http://www.sosmath.com/algebra/logs/log1/log1.html

http://www.purplemath.com/modules/logs.htm

http://www.shodor.org/unchem/math/logs/index.html

http://www.youtube.com/watch?v=mQTWzLpCcW0

And, just for old time's sake :

Nonagon Song - http://www.youtube.com/watch?v=x5ohtlewREI

One Dozen Monkeys -http://www.youtube.com/watch?v=2qdql9vsWWM&feature=related

Hope this helped and made logarithms a little less unbearable :)

Bye, Katie 

3.1 to 3.3

Hi. The stuff covered in 3.1 to 3.3 is pretty much all things we have already learned. The first concept covered is the Cartesian Cordinate system with a x-axis, a y-axis, and four quadrants pictured below.



The next thing covered is the distance formula . The distance between any two points (x₁, y₁) and (x₂, y₂) is



The distance formula can be proved drawing a right triangle between points and finding the length of the hypothenuse using the Pythagorean Theorem as shown below.



Next we learned about the Midpoint formula. The midpoint of the line segment from (x₁, y₁) to  (x₂, y₂) is

This can be proved because the x-cordinate of the midpoint is equal to the average of the x-cordinates of the endpoints. The same goes for the y-cordinate. That's pretty much everything in 3.1.

3.2 deals with the graphs of equations. We went over some basic terminology.
     Solution: And ordered pair that yeilds a true statement
     X-intercepts: The x-cordinates of the points where a graph intersects the x-axis
     Y-intercepts: The y-cordinates of the points where a graph intersects the y-axis
You can find the x-intercept of a function by substituting the y value with 0. You can find the y-intercept by substituting the x value with 0.

The next thing covered is graphs of circles. The standard equation of a circle with center (h,k) and radius r is

Keep in mind that circles are not a function because they don't pass the vertical line test. If you want to graph a circle on your graphing calculator (which only graphs functions) you can graph two semicircles. All you have to do is solve the equation for your circle for y, which will lead you to two answers (±). For y1 enter the positive value of the equation and for y2 enter the negative value.

3.3 goes over lines

The slope of a line is defined by the formula

If the line is parallel to the y-axis, then the slope is undefined. A line parallel to the x-axis has a slope of 0.

Another important equation is the Point-Slope Form. An equation for the line through point  (x₁, y₁) is 

y – y₁ = m(x – x₁)

The books also talks about standard form (ax+by=c) which Mr. Wilhelm said we don't have to know.

We also went over relationships between lines.

Two nonvertical lines are parallel if and only is they have the same slope and two lines with opposite reciprical slopes are perpendicular.

Well thats pretty much everything. Bye.

     -Corn Murphy

Section 2.1

Hello fellow class members, first i am produce to announce that book licker has been accepted into urbandictionary.com, http://www.urbandictionary.com/define.php?term=book%20licker will be up very shorty.

This section in the book has to do with equations. Woohooooo!!!!! And overall this section is what we learned in 8th grade (or 7th for the chosen ones) but it just takes it into the next level of difficulty.

Equation- a statement where two quantities or expressions are equal. like the one my dad has tattooed on his back.

or one as simple as y=mx+b, but thats not as fun......

Algebraic equation- contain algebraic expressions such as polynomails, rational expressions, radicals and so on.

Conditional equation- same as above but if there are numbers in the domains of the expressions that are not solutions like 16=x^2

Identity- An equation where every number in the domains of the expressions in an algebraic equation is a solution..... 2x+64=2(x+32)

Solving an equation

(2x+5)(5x-3)=4x+10 simplify 4x+10

(2x+5)(5x-3)=2(2x+5) take away 2x+5 on both sides

5x-3=2 add three on both sides

5x=5 divide

x=1

An equation containing rational expressions

http://tutorial.math.lamar.edu/Classes/Alg/RationalExpressions.aspx

the website above sums it all up completely

http://www.onlinepoker.net/poker-news/casino-news/casino-cheats-caught-rigging-roulette-spin/10772 coincidence of Birmingham Crown Court????

Boom! Game

Thank you,

Peter Kessel