### Scribe: Introduction to Exponents and Logarithms

Well today was a two day, and lucky me, I got chosen for it fair and square.

Let's see, well the morning started off with Mr. K telling us things to know and expect, when doing something for the first time. Like riding a bike, or in this case dealing with math. Since you're doing it for the first time, you can't expect to learn it right a way, you're going to have to work at it.

**Education is about pushing yourself**, to that level where you're not just satisfied, but to that level of excellence.

Then Mr. K put us into groups, where we had to solve probability questions.

**1. Two soccer teams, A and B, have a kickoff to see which team wins the game. The teams take turns to attempt to score a goal. The first team to score wins. The probability of team A winning with one kick is 0.20. The probability of team B winning with one kick is 0.25.**

a) Suppose team A kicks first. What is the probability that team B wins on its first kick?__First Kick__**AN*BG****(0.8)(0.25)= 0.2****=20%**

b) Suppose team A kicks first. What is the probability that Team A wins on it's third kick?__1 ^{st}, 2^{nd}, 3^{rd} kick__

**(AN*BN)(AN*BN)*(AG)**

**(0.8*0.75)(0.8*0.75)(0.2)=0.072**

=

**7.2 %**

**2. Five dimes and five nickels are arranged in 3 boxesas follows: Box 1 has 2 nickles and a dime, Box 2 has 2 nickles and a dime, Box 3 has 3 dimes and a nickel. A box is randomly selected, then a coin is randomly selected from that box. **

What is the probability that the coin will be a nickel?

P(1N)= 1/3 * 2/3

= 2/9

P(2N)= 1/3* 2/3

= 2/9

P(3N)=1/3* 1/4

=1/12

P(N) = P(1N) + P(2N) + P(3N)

= 2/9 + 2/9 + 1/12

=8/36 + 8/36 + 3/36

=19/36

**3. A hand of 13 cards is dealt from a shuffled deck of 52 cards. What is the probability that there are:**

b) at Most 5 spades?

Then comes our introduction to the new unit in the afternoon; **Exponents and Logarithms**. These are some basic stuff we should already know about exponents:

Then Mr. K gave us four numbers on the board. We had to write each of them 4 different ways using only exponents.

***A number can be written in many different ways.

These were the numbers

__ 4__(1/2)

^{-2}

(16)

^{1/2}

(1/4)

^{-1}

(1/8)

^{-2/3}

** 1/2**(2)

^{-1}

(4)

^{-1/2}

(1/4)

^{1/2}

(8)

^{-1/3}

** 3**(1/3)

^{-1}

(9)

^{1/2}

(1/9)

^{-1/2}

(27)

^{1/3}

** 3/4**(4/3)

^{-1}

(9/16)

^{1/2}

(16/9)

^{-1/2}(27/64)

^{1/3}

***Any base __must__ be in reduced form!!

Of course there is a pattern into figuring the different ways of writing a number. Using the basic stuff to find the first couple of ways, then you can use that to help you find the pattern.

Then Mr. K gave us another type of question on the board that had to deal with a variable in the exponent.

Here's another question Mr. K gave us, that I should warn you about.

It is common that people will do this in the next question:

3(5^{x+1})= 15

15^{x+1}= 15

Because of BEDMAS, exponents should go first before multiplying,

YOU CAN'T RAISE 5 TO THE EXPONENT X +1

So it is solved like this,

3(5^{x+1})= 15

5^{x+1}= 5

x + 1 = 1

x= 0

Double check:

3(5^{x+1})= 15

3(5^{(0)+1})= 15

3(5^{1})= 15

3(5)= 15

15=15

Mr. K gave us many practice questions, so here they are along with the answers:

**Q.**27^{x}= 9^{2x-1}^{A. x=2}

**Q.**4^{2x-1}= 64

A. x=2

**Q.** 32^{3x-2}= 64

A. x= 16/15

**Q. **4^{8x}= 1/16

A. x= -1/4

**Q. **6^{3x-6}=1

A. x=2

**Q.** 5^{4-x}= 1/5

A. x= 5

**Q.** 3^{2x-1} + 1 = 2

A. 1/2

I just want to say, very sorry guys for the late scribe, but i FINALLY FINISHED.

Okay well thats about it for the two classes today, for the people who weren't in class there wasn't any dictionary notes for today. Oh and there's a pretest tomorrow. Also Homework was page 89 1-16 and 24.

The lucky scribe for tomorrow is Zaenab.=)

^{}

## 2 Comments:

Hi Jacky,

Congratulations on a job well done!! I really like your emphasis on "don't do that" to help keep everyone on track and away from a common mistake.

You and your classmates are truly traveling on a path of excellence!! I wonder, can you all meet the challenge of a daily "hall of fame" scribe through to the end of May??

Best,

Lani

What an extraordinary job you and your classmates are doing. Your explanation is fascinating and just reading your material is an education for me. I plan to use your blog as an example excellence in some workshops I am doing for teachers in upstate New York.

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