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 about

how important it is for us to be doing our homework

during this unit. He says that this is the TOUGHEST

unit, and that he’s been trying to give us various

tools to help us through, but if were not doing the

homework we’re not getting what we need. Mr. K really

wants us all to give the effort to do our homework because

he doesn’t want to see anyone fail, so lets pull

up our socks and do our best to catch up.

Next Mr. k gave us a quiz, in which we were allotted 12

minutes 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 -3

2. Find log 2(64) + log 3(9)

log 22^6 + log 33^2

6 + 2

8

3. 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 these

Answer: B

log a25 = 4

a^4 = 25

(a^4) ^ 1/4 = 25 ^1/4

a= √5

5. Find the log 100(1000000)

log 100(100^3) 3

6. Find log 100(10)

log 10010 log 100(100)^ 1/2 1/2

After the time was up Mr. K put all of these answers

on the board and asked students which ones everyone

wanted explained.

When he was finished explaining, he began telling us

about how math is hard, and that this course is one/or

the most difficult class in our high school career.He

believes 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 skims

the rim and goes in, we just need to get that basket

(answer). Our attitudes are hurting us as just getting

the answer is not developing our skills for seeing

things from many angles. If we were to learn things so

that we can see the answer, or know the tools we need to

find the answer from many different angles, this unit

would be easier, and we would know the answers instead

of getting lucky.

Mr. K also told us that he wasn’t giving us a quiz to

punish us for not doing our homework, but that he knows

that students who do there homework and have quizzes to

make sure they are on the right track, do better in

the end. Basically

“NOT DOING YOUR HOMEWORK HURTS”

It is easy to give us marks on things like scribe posts

andassignments where people post comments, because their

learning is evident. But when students don’t do their

homework and then do poorly on quizzes, their learning

isn’t evident,and results are low marks.

The mark that you receive is not a measure of how smart

you 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 doing

homework,class discussions,or tests/quizzes then you

will never get up to your full potential, and your

mark will reflect it.

If you want a good mark

PUT THE TIME, ENERGY, AND EFFORT IN!!

PUT THE TIME, ENERGY, AND EFFORT IN!!

Mr. K then moved on to explain that what we are doing

now are simply the mechanics of logarithms. We are

learning the manipulations, and basics so that we master

them before going on to the more difficult and

“interesting” problem solving section of the unit

(starts Monday).Your basic skills must be STRONG,because

there is no time to waste on worrying if your mechanics

are 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 Logarithm

1. log a2 + log a3 2. log b4 + log b5 – log b2

3. ½(log cX + log cY)

Expand

1. log 2(MN) 2. log 2 M/N

Solve

1. log aX = 2log a3 + log a5

2. log cX – log c(X-5) = log c6

3. log aX = 3/2 log a9 + log a2

Answers:

Write as a Single Logarithm

1. log a2 + log a3

log a(2x3)

log a 6

2. log b4 + log b5 – log b2

log b (4x5)/2

log b 10

3. ½(log cX + log cY)

logc √XY

Expand

1. log 2(MN)

3 (log 2 MN)

3 log 2 M + 3 log 2 N

2. log 2 √M/(N^3)

1/2 log 2M + 3/2 log 2N

Solve

1. 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 c6

log c(X / X- 5) = log c6

X = 6X - 30

-5X = -30

X = 6

3. log aX = 3/2 log a9 + log a2

log aX = log a9∧3/2 + log a2

log aX = log a27 + log a2

log aX = log a54

At the end of our first class Mr. K put these questions

on the board, told us to do what we could, and gave

us a couple minutes before the bell to finish them.

log 3(X+2) + log 36 = 3 log 6(X+1) + log 6X = 1

2 log 3X - log 3(X- 2) = 2

For the answers to these questions scroll down :D

After 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 2∧ log 2 (17)

5) Find 4 ∧ log 2 (3)

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 2∧ log 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--> 3

log 10(200)

log 10(2x1000)

log 102 + log 101000

0.301 + 3

3.301

3 is closest to 3.301

2) c--> 0.9

log 108

log 102∧3

3 log 102

3 (0.301)

0.903

3) c--> 3

Reason it out...

2∧3= 8 --> is the closest to 10...

the exponent for this

is 3... therefore the answer is 3

2∧4= 16

or

log 102 = 0.301 log 210 = X

10 ∧ 0.301 =2 2∧X = 10

(2∧x) ∧ 0.301 = 2∧1

0.301X = 1

X = 1 / 0.301

4) 17

if x =17 is the answer of log2 X = 17

notice 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

2² ∧log 23

2 ∧ log 23²

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??

We reject negative numbers because

*ALL IMPUTS MUST BE POSITIVE*

-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

can receive marks?

-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....

2∧3 = 8

log 2 8 =3

could be written as: 2∧log 2 8 = 3

Back on track..

5) 9

4 ∧log 23

2² ∧log 23

2 ∧ log 23²

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 = 1

log 6 [ (X=1)x X] = 1 In this case there

X² + X = 6 is no exponent of

X² + 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) = 2

log3X² - 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. KDo we think that del.icio.us is a useful tool?

started talking about our homework from last night

(making a del.icio.us account,and finding 4 sites

1 for each unit we have studied. After a brief

talk,we began another round of questioning:

-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

can receive marks?

-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

Best of Luck

Hi Lisa,

ReplyDeleteYou 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

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

ReplyDeleteKeep it up.

I agree. This is hall of fame worthy.

Chris

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!

ReplyDelete~HALL OF FAME~

bbye

This is ubber cool heh,

ReplyDeleteI 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

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!!!

ReplyDeleteWow! 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

ReplyDelete