## November 02, 2006

Ok guys, I guess I’m your scribe today, so lets get to it shall we….

`When we first got to class, Mr. K began talking abouthow important it is for us to be doing our homeworkduring this unit. He says that this is the TOUGHESTunit, and that he’s been trying to give us varioustools to help us through, but if were not doing thehomework we’re not getting what we need. Mr. K reallywants us all to give the effort to do our homework becausehe doesn’t want to see anyone fail, so lets pullup our socks and do our best to catch up.Next Mr. k gave us a quiz, in which we were allotted 12minutes to finish six questions.The questions were:1. Find log 10(0.001)log 10 1/ 1000 log 10 (1 / 10^3) log 10 10^-3 -32. Find log 2(64) + log 3(9)log 22^6 + log 33^26 + 283. If 3^ X = 7, which is true?a) 7 = log X (3) b) x= log 7 (3)  c) 3 = log x (7)d) 7 = log 3 (x) e) x = log 3 (7) f) 3= log 7 (x)Answer: E`
* A LOGARITHM IS AN EXPONENT*
`4. If log a(25)= 4, what is a?a) 1/ 5  b)√5  c)5 d) log 2 5 e)none of theseAnswer: Blog a25 = 4a^4 = 25 (a^4) ^ 1/4 = 25 ^1/4a= √55. Find the log 100(1000000)log 100(100^3) 36. Find log 100(10)log 10010 log 100(100)^ 1/2 1/2After the time was up Mr. K put all of these answerson the board and asked students which ones everyonewanted explained.When he was finished explaining, he began telling usabout how math is hard, and that this course is one/orthe most difficult class in our high school career.Hebelieves that most of the students have the attitude “I just need to get by” or “I just need to get this answer”just like the players who throw the ball and it skimsthe rim and goes in, we just need to get that basket(answer). Our attitudes are hurting us as just gettingthe answer is not developing our skills for seeingthings from many angles. If we were to learn things sothat we can see the answer, or know the tools we need tofind the answer from many different angles, this unitwould be easier, and we would know the answers insteadof getting lucky.Mr. K also told us that he wasn’t giving us a quiz topunish us for not doing our homework, but that he knowsthat students who do there homework and have quizzes tomake sure they are on the right track, do better inthe end. Basically`
`It is easy to give us marks on things like scribe postsandassignments where people post comments, because theirlearning is evident. But when students don’t do theirhomework and then do poorly on quizzes, their learningisn’t evident,and results are low marks.The mark that you receive is not a measure of how smartyou are,instead it is a measure of three aspects:-Your time-Your energy-Your effort`
`If you do not put in these three aspects when doinghomework,class discussions,or tests/quizzes then youwill never get up to your full potential, and yourmark will reflect it.`
If you want a good mark
PUT THE TIME, ENERGY, AND EFFORT IN!!
`Mr. K then moved on to explain that what we are doingnow are simply the mechanics of logarithms. We arelearning the manipulations, and basics so that we masterthem before going on to the more difficult and“interesting” problem solving section of the unit(starts Monday).Your basic skills must be STRONG,becausethere is no time to waste on worrying if your mechanicsare wrong when you are doing a problem solving question.Next Mr. K put these questions up on the board*Don’t look at the answers before you’ve tried them yourself*Write as a Single Logarithm1. log a2 + log a3    2. log b4 + log b5 – log b23. ½(log cX + log cY)Expand1. log 2(MN)     2. log 2 M/NSolve1. log aX = 2log a3 + log a52. log cX – log c(X-5) = log c63. log aX = 3/2 log a9 + log a2Answers:Write as a Single Logarithm1. log a2 + log a3    log a(2x3)              log a 6                        2. log b4 + log b5 – log b2log b (4x5)/2log b 103. ½(log cX + log cY)logc √XY Expand1. log 2(MN)         3 (log 2 MN)         3 log 2 M + 3 log 2 N2. log 2 √M/(N^3)1/2 log 2M + 3/2 log 2NSolve1. log aX = 2log a3 + log a5    log aX = log a3² + log a5    log aX = log a9 + log a 5      log aX = log a(9x5)         log aX = log a45      2. log cX – log c(X-5) = log c6log c(X / X- 5) = log c6X = 6X - 30 -5X = -30X = 63. log aX = 3/2 log a9 + log a2    log aX = log a9∧3/2 + log a2log aX = log a27 + log a2log aX = log a54At the end of our first class Mr. K put these questionson the board, told us to do what we could, and gaveus a couple minutes before the bell to finish them.log 3(X+2) + log 36 = 3      log 6(X+1) + log 6X = 12 log 3X - log 3(X- 2) = 2For the answers to these questions scroll down :DAfter lunch.... it was Quiz time: `
Ok guys... clear your desks, you can have a pencil,
you canhave an eraser, you can have a lucky charm,
their magically delicious, you can even have a lucky
rabbits foot, but not a real rabbits foot cause that's cruel.

*Here are the questions, try to answer them before you look at the answers below*

1) if log 102 ≈ 0.301, which of these is the closest to log 10(2000)?

a) 0.6 b) 3 c) 6 d) 30 e) 60 f) 300

2) if log 10 2 ≈ 0.301, which of these is closest to log 10 (8)?

a) 0.3 b) 0.6 c) 0.9 d)1.2 e) 2.4

3) if log 102 ≈ 0.301, which of these is closest to log 2(10)?

a) 0.5 b)1 c) 3 d)5 e) 20 f) 50

4) Find 2log 2 (17)

5) Find 4 ∧ log 2 (3)

`6) if log3 (10)= K, then log 9(10) =?Twelve minutes up... time to take up the quiz...Quiz Answers:1) b--> 3log 10(200)log 10(2x1000)log 102 + log 1010000.301 + 33.3013 is closest to 3.3012) c--> 0.9log 108log 102∧33 log 1023 (0.301)0.9033) c--> 3Reason it out...2∧3= 8 --> is the closest to 10...the exponent for this  is 3... therefore the answer is 32∧4= 16orlog 102 = 0.301    log 210 = X10 ∧ 0.301 =2     2∧X = 10(2∧x) ∧ 0.301 = 2∧10.301X = 1X = 1 / 0.3014) 17if x =17 is the answer of log2 X = 17notice that the large 2 is also a base 2,therefore the answer is 17*SIDE BAR*`
*A LOGARITHM IS AN EXPONENT*

2∧3 = 8
log 2 8 =3
could be written as:
2∧log 2 8 = 3

Back on track..

5) 9

4 ∧log 23
2
² ∧log 23

2 ∧ log
2

2
∧ log 29

9

6. k /2

log 210 = k find log a10 = X

3∧k= 10 9∧X = 10

3∧k = 9∧ X

3∧k = 3∧2X

K= 2X

K
/ 2 =X

And that's it for the quiz folks... don't feel bad if you didn't
do well, the majority of the class seemed to be having
trouble... but if you did do well give yourself a pat on
the back....

After the quiz and the take up, Mr. K asked the class
some questions...

Who learned something?

- the majority of the class raised their hands

Who would have done better if they had done there
homework?

- a handful of honest students raised their hands

Next Mr. K asked us to finish the questions that were on
the board before lunch...

remember these from above??
`log 3(X+2) + log 36 = 3  log 3∧ [ (x+2) x6] = 3       (x+2)6 = 3∧3                6X + 12 = 27                 6X = 15                              log 6(X+1) + log 6X = 1log 6 [ (X=1)x X] = 1      In this case thereX² + X = 6                 is no exponent ofX² + X - 6 = 0                   6 can give an output(X+3) (X- 2) = 0               of -2, therefore X= - 3  X = 2                    NO NEG. #'s CAN Reject  X= -3                    BE USED`

We reject negative numbers because

*ALL IMPUTS MUST BE POSITIVE*
`2 log 3X - log 3(X- 2) = 2log3X² - log 3(x- 2) = 2 log 3 [X²  / (X-2)] = 2 (x-2) x [ X² / (X-2)] =2 X² = 9 - 18 X² - 9X + 18 = 0 (X- 3) (X- 6) = 0 X = 3  X= 6`
BOTH ARE POSITIVE, THEREFORE BOTH ARE THE ANSWERS

`After we finished taking up the questions, Mr. Kstarted talking about our homework from last night(making a del.icio.us account,and finding 4 sites1 for each unit we have studied. After a brieftalk,we began another round of questioning:`
Do we think that del.icio.us is a useful tool?
-yes

Do you think it would be more beneficial if students took 15-20
mins to find a site that actually
helped them understand
concepts rather than just picking the first site they find so they

-yes

If you take the time to find one helpful site, and your class mates
take the time to find helpful sites then for your imput of 1 site you
get 22 in return. Is this beneficial to you?

-yes

We kind of got the point across that getting help is more important, then marks
so when he asked the question

Who thinks that you should be marked on your contribution to del.icio.us ?

-no one raised their hands

Ok guys time to step it up a notch...

Mr. K then put much more challenging equations on the board and asked
us to solve them:

1. log b (X-1) + log b (X+2) = log b (8 - 2X)

log b [(X- 1) (X+2 )] = log b (8 - 2X)

X² + X -2 = 8 - 2X

X² + 3X - 10 = 0

(X + 5) (X- 2) = 0

X= -5
X= 2

REJECT NEGATIVES

2.log 10 (X+ 6) + log 10 (X-6) = 2

log (X² -36) = 2

X² - 36 = 100

X² - 136 = 0

X = √136

2^X = 7 5^X = 11 Find X

log 2X = log 7

X log 2 = log 7

X = log 7 / log 2

*NO BASE WRITTEN MEANS THE EQUATION IS USING BASE 10*

After taking up these questions, Mr. K started the final topic of
the day....

Base Values

We use the base value 10

therefore we have 10 base numbers

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The number ten is represented by 10.... as the first numbers all begin with zero, the next set of ten will begin with one, and so on.

11, 12, 13, 14 etc.

the pattern continues as you move forward, the next set will begin with twos

20, 21, 22, 23 etc.

this pattern continues all the way through our number system.

Another way to look at this is :

This uses 10 as the base number and grows from there

another example of this is
1 x 10^2 = 100
2 x 10^1 = 20
3 x 10^0 = 3

100 + 20 + 3 = 123

But if we were to use a base of 6 instead for example, we would only have 6 numbers

0, 1, 2, 3, 4, 5

6 would be represented as 10

and 7 would be represented by 11, following the pattern:
Therefore using the base number 6, the number we know as 123 in base ten would actually equal 51 in base 6,
1 x 6^2 = 36
2 x 6^1 = 12
3 x 6^0 = 3

36 + 12 + 3 = 51

That's where class ended today folks... i know its a lot, but ALL of it was important.... I hope
this post was helpful for you!! Good luck guys!!

Ok well i guess the next scribe will be....

*ALLEN*

Best of Luck

1. Hi Lisa,

You are absolutely right!! It is all important!!

That you included the critical discussions on effort and del.icio.us prompts me to suggest that this may be Hall of Fame worthy!

Any time you and your classmates need to "step it up a notch", in effort or in skills, you will be able to return to this scribe for encouragement!!

Best,
Lani

2. An excellent post. I could feel the emotions in your class through your writing.

Keep it up.

I agree. This is hall of fame worthy.

Chris

3. wow!!!! good job lisa, well done! your post have so many good information about logarithm that i think i will tag this to my delicious account and read it for review in the future!

~HALL OF FAME~

bbye

4. This is ubber cool heh,
I have one thing to say and a question....

1)Welcome to the Hall of Fame!!!
2)and how long did this monster take to finish?

Bye

5. you got my vote to get you in the hall of fame,you've pushed the bar s high, that the bar has added to 200 lbs!!!

6. Jennifer Jolly7/25/2013 12:51 PM

Wow! You have been placed in a book, Who Owns the the Learning, studied by educators. You had an awesome teacher. I would say you own it! Jennifer Jolly, Texas