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
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