Thursday, December 10, 2009

HW

Purplemath.com log links (scribe?)

HW:

  • Choose 8 problems from the Chapter 3 Review/Test. Include them with your homework packet.
  • Organize your homework- make sure each assignment is completely checked and corrected and that each has your name, date, and the assignment at the top. Stack your homework ordered from oldest to newest with the homework cover page on top. Staple your stack in the lower right hand corner. You will hand in your homework on the day of the test before you take your test.
  • Revise for the test. Rest. Psych yourself up. Don't be late and don't be sick- Monday is game day...

Tuesday, December 8, 2009

Scribe Post 8.12.09

We started off with reviewing our Quiz from last class, and our Homework from last class. Then we took a Quiz regarding Log's. Our Quiz lasted for most of the class, but then we moved on to the next chapter.
We started off on pg.265, with problem #26 concerning the half-lives of Radon, and graphing the function y=ae^(-bt), where t is the length of time, b is the horizontal dilation, a is the vertical dilation, and y is the final value of the Radon. We subbed in values as t=1599, y=50, a=100, and then calculated for b, which was b=ln(1/2)/-1599. We then reversed our process, and calculated a with the values of 1.5=ae^-1000[ln(1/2)/-1599], which gave us the value of a=2.3g. We then filled in the values on TI-SmartView, which graphed the equation as a decaying function.
We then confirmed that the function did match the graph. Our homework deals with these functions tonight, but we don't have to memorize the functions for a test.

Next times scribe is Molly.
HW:

* p. 265/15, 17, 19, 25, 27, 35, 39, 41, 43, 45, 51, 55, 59, 63

Monday, December 7, 2009

Tyler's Late Post

In class on Friday we took the first quiz on chapter 3 and then we went over our homework on pg. 253. The majority of the class time was consumed by the quiz. We did not go over any new materials, however we stressed a few laws of log to remember for the next quiz (which is tomorrow).

Notable Points:

1. The base property:
log_{2} 5 = \frac{log_{5} }{log_{2} }

2. ln=e

I hope the class found everything else easy to follow with log. I apologize for the post being so late, most likely it wasn't any help to any of you. Homework for tomorrow is to study for the quiz. Review the HW from pg. 243, and 253 to study. There is also a HW assignment on pg. 253 due for tomorrow. Good luck to everybody on the test.

Here is a website that looks very useful for studying the rules of log: http://www.themathpage.com/aPreCalc/logarithms.htm

Friday, December 4, 2009

HW:

* p. 253/101, 97, 95, 91, 87, 59, 55, 53, 39, 33 (whichever are not finished in class)
* Be sure other homework is up to date

Wednesday, December 2, 2009

Unit 3 Logarithms, Scribe Post

Today we began class by a quick discussion of the mid-term, Mr. O’Brian mentioned that some of the questions on the test will be multiple choice. He also mentioned that students need to understand the concepts we have gone over so far this year.
Next we looked over the Unit 2 test, Mr. O’Brian stressed that students check all answers and make sure that you answer the question that is being asked. When your are supercorrecting pick apart the problem, see how many connections you can make, and show many different ways you can solve it. One note to make is anytime you have a test question concerning a function, you need to have a equal sign and function name with the solution. Mr. O’Brian explains that the questions on the supercorrection follow-up test are the problems he believes to be the most important, the problems he wants to “stick” in student’s minds.
Next, we took notes on the Big Three Log Properties. The first is
Log_{p} a\cdot b=Log_{p} a+Log_{p} b. The seconds is Log_{p}\frac{a}{b} =Log_{p}a-Log_{p}b   . The third is Log_{p}a^{n}= n\cdot Log_{p}a .

Next we created a proof for:
Log_{p} a\cdot b=Log_{p} a+Log_{p} b.
Proof:
Let
u=Log_{p}a and v=Log_{p}b
So: p^{u}=a p^{v}=b
Multiply: p^{u}\cdot p^{v}=a\cdot b
Simplify: Log^{u+v} =a\cdot b
Log_{p}a\cdot b=u+v
Therefore:
Log_{p}a\cdot b=Log_{p}a+Log_{p}b
Q.E.P.

We next proved the second of the Big Three Log Properties which is similar to the first proof but changes the multiplication and addition.
The third proof is almost similar to the second property applied multiple times. Mr. O'Brian said that for bonus, students should prove the third Log property.
Next, we looked at the other log properties on page 230 of our textbooks. Mr. O’Brian said that students should say the properties out loud in words to make sense of them.

We took notes on the Change of Base Formula which is
Log_{p}a=\frac{Log_{b}a}{Log_{b}p }   .
Proof:
Log_{p}a=u
Take the log of both sides: Log_{b}p^{u}=Log_{b}a
u\cdot Log_{b}p=Log_{b}a
u=\frac{log_{b}a}{Log_{b}p }
Therefore: Log_{p}a=\frac{Log_{b}a}{Log_{b}p }
Q.E.P
In the last 15 minutes of class Mr. O'Brian let us work on the homework problems.

Next Class: Mr. O’Brian noted that students should check their answers for the homework to prepare for the quiz because “there is no fudging with logs”. Quiz on friday will be non-calculator. Mr. O'Brian said that for bonus, students should prove the third of the Big Three Log Properties.

Tyler will be the next class scribe
HW:

* p. 243/47-59 odd, 69-79 odd, 80
* p. 253/12, 14, 30, 56, 86, 94
* p. 253/9-23 odd, 27, 29, 35, 49, 57, 65, 81, 93, 99
* Look over your homework in preparation for the quiz next class