reflection 6

This week wasnt that bad i actually understood everything that was going on...

Changing Bases
-used when a log cnt be solved
- used to solve for x as a variable
-used to change the base of a log
1.write as exponetial form
2. take the log base of both sides
3.move exponents to the front
4. solve for variable
5. write as a function or whole number if possible.
*If not possibnle leave in log form...

solve
log base 3 of 7
1. 3^x=7
2. log 3^x = log 7
3. x log 3= log 7

divide both sides by log 3 to get x by itself .

x=log7/log3 would be you final answer.

solve
5^x=10
since the first step is already done for you move to step 2
log 5^x = log 10
x log 5 = 1

the reason for log 10 being 1 is bc the base of a log is understood to be 10

the divide to get x by itself and it would be

x=1/log 5

Reflection #5

Last week was kind of difficult, however, one thing that i really got the hang of is putting logs in exponential form.

For example: log base b of a set equal to x.

To put it in exponential form would look like this: b^x=a

And then you change a to the same base as b.

The exponent of a would then be equal to x.

reflection 5

Ok, sorry this came in so late, but i had a looooooooong weekend. Ok, first things first, woohoo, the football team won :D. What was the score, like 22-13 i think. Meh, from what i hear, the band sounded good. To tell you the truth, our band has potential, but we are still trying to get the whole act together, and will hopefully be waaay better in the near future. I mean, sound better, act better, look better, all of that and MORE! hahaha. So to now to a different subject. This weekend, i went to a religion retreat. I know, it sounds boring. That's what i thought. But guess what. It was actually fun. :D We did alot of stuff, like some rope challenge thing where we had to work together to overcome obstacles (i know, it still sounds boring and retarded, but if y'all go to a confirmation retreat to Camp Istrouma, then u'll know what im talkin about), we got locked out of our dorm, thanks to brandon, we definately saw different sides to some people that we never knew existed. This retreat opened ME up to God, i dont think anybody knew if it was possible, but i did open up to God. It really was an experience that i encourage people to go on, not just to be able to go to confirmation, but to actually open up. We got letters from our family members that broke us down. One of mine hit me HARD, RIGHT DEAD IN THE CENTER OF MY HEART. I literally went back to my dorm, and just sat there for about 10 minutes reading and sobbing over that letter. umm........ Back to a new note! I won one of the 2 spirit awards, which were too stuffed cats named wampascat and leeroy dudley. I got leeroy XD. And we got these necklaces that have a wooden cross on them, i actually havent taken mine off since i got it, besides when i shower. But really, its a great experience, and anyone who went or is going, u know what im talkin about. O, another thing. We stayed up till like 6:30 am the night of the retreat, so when i got home the next day, i was waaaaaaaaaay too tired to do this reflection. sorry.

Anyway, back to math.

one thing i did understand was how to do logs.
it was like log(base 2) 8=x
to do this, put it in exponential form, 2^x=8
then, change the base so that they're the same, 2^x=2^3
then, get rid of the bases so that u only have the exponents left to solve and get, x=3

but one thing i didn't get was for exponents,
do u distribute the exponent or use foil when u do something like (a^2+b^4)^-3


also, here's the comments that ive been putting over the last few weeks, if that's what u told me to do in class,
this week: http://br0910advmathhonors.blogspot.com/2009/09/reflection-5-redo.html?showComment=1253660385103#c1750677111025477040

http://br0910advmathhonors.blogspot.com/2009/09/reflection-5_324.html?showComment=1253660567538#c4807719554302567703

then last week: http://br0910advmathhonors.blogspot.com/2009/09/reflection-4_2644.html#comments

http://br0910advmathhonors.blogspot.com/2009/09/reflection-4_569.html#comments

and the week before that i had one, but at least i did it: http://br0910advmathhonors.blogspot.com/2009/09/pleas-help-with-4-on-packet.html#comments

yea, that's all of them that i couldnt get u to c b/c my email is blah right now

and if u could, can u post ur email address so that i can see if im just typing it in wrong, or my email is messin up all together

Reflection #5

I understood logs very well this week.

When it asks for you to put it in exponential form all you do is swoop out the last new numbers.

For example:

log4^3=31

Your answer would be: 4^31=3

(Not a true statement but just an example)

When it asks for logarithmic form you would just do the opposite..

Example:

6^8=12

log6^12=8

log base is always understood as 10...

on the other hand, I do not understand what our quiz is on Monday...

I'm completely lost!

Reflection 5

Well this week was pretty difficult. I definitely have some studying ahead of me.
Firs off, Logs. They are pretty easy.
logb^x=a
all you would do is switch the x and the a.
b^a=x (exponential form)

log3^2=7
3^7=2

This helps you solve problems sometimes.
But before you solve you have to change it to exponential form.

Example:
logx^4=2
x^2=4
x= +/- 2

For natural logs-
e^x=75
change e to ln(natural log), then switch the x and the 75
ln75=x
Plug into your calculator.
ln 75=4.317

So logs are not so hard.

Now exponent rules on the other hand give me a little struggle.

I'll just give a couple examples of solving exponents.

x^3/5=5 square roots of x cubed (rule number 6)

5^x-1=1/125
5^x-1=125^-1
5^X-1=5^-3 (now that the bases are equal you can set the exponents equal to each other)
x-1=-3
x=-1
( rule 7)

reflection 5

so i dont even remember if this week went by fast or slow. i dont even remember everything that we learned this week. the only thing i remember is the log stuff and the e^exponent stuff.
that was reallllyyy easy. im proud of myself that i actually understood it. oh, and another thing about this week, the chapter test was soo short. i really think i did good on it (ha, watch me make like a 62) so here are some examples of logs...



EXAMPLE 1:

logx^4=2
x^2=4
x=+/-2

Reflection #5.

Well, this week obviously didn't end well for me. Unexpected flu, yuck!
Anyways, what i learned BEFORE i was called out of class included exponential equations, I'll try and explain those to the best of my ability:

in an equation:
(b^2/a)^-2 TIMES (a^2/b)^-3

you must first distribute your exponents to all parts of your fraction, in the case of exponents, you must multiply the exponential values together, i.e.,

(b^-4/a^-2) TIMES (a^-6/b^-3)

in order to remove all negative exponents from the equation, put a 1 over each and use the sandwich method!

(1/b^4)/(1/a^2) TIMES (1/a^6)/(1/b^3)

multiply the top by the bottom(BREAD) and the two inner fractions by each other(MEAT, or peanut butter- whichever you prefer. lol)

a^2/b^4 TIMES b^3/a^6

cancel what you can:

a^2 and a^6= a^4
b^4 and b^3= b


FINAL EQUATION:

1/ba^4


---------------------------------------------------------------------
On the contrary,
fractions and radicals exponentially?
I was able to copy half of the notes before i left and i'm definitely stuck in the dark!

ANY HELPERS?! :)

Reflection 5

This week went well and it was quite easy. The chapter test wasn't really big so that was tight. The second half of the week we learned about logs and exponential equations. I thought logs were extremely easy. They samed easier that last year.

Examples of some logs:

log 7 of 49 = 2 log x of 36 = 2
7^2 =49 x^2 = 36
x = 6

log 3 of 27 = 3 log x of 64 = 3
3^3 =27 x^3 = 64
x = 4

log 2 of 32 = 5 log x of 100 = 2
2^5 =32 x^2 = 100
x = 10

Now I get the main concept of solving for exponents but I am never sure when the problem is simplified all the way. There are so many little steps.

Reflection#5

This week in advance math was pretty easy. I was a little diappointed in my test grade because i did some simple mistakes that got me a bunch of points taken off the multiple choice. We learned how to solve with exponents. When multiplying with exponents you add the exponents. When dividing by exponents, you subtract the exponents. when you have two different variables you just put the exponent to the variable you are multiplying or dividing. To solve for an exponent you write as the same base, set exponents equal, and then solve for x. We learned how to solve by a negative exponent. You put 1 over that number and exponent. We also learned the sandwhich method which is done when you have to fraction over each other than you multiply the first and last then the two middles. We also learned how to solve for LOGS. LOGS are easier than what i thought, i learned that very easily. On the homework they also had how to solve for the rate of interest. I pretty mush understood everything this week. I hope that this week is just as easy.

reflection 5 redo

This week wasn't that bad. The week went by pretty fast surprisingly, the Chapter 4 test was okay but I didn't really study so i think i might have done worse that i think. In class, we learned a lot about exponents and we started learning about logs and solving for them.

Example:

(a^2/b)^-2 times (b^2/a)^-3

You have to distribute the ^-2 and ^-3 to both terms on their respective fractions. When there is an exponent inside parentheses, and another one outside, you multiply them together. When there is an exponent inside parentheses, and another one inside another parentheses, or both together, you add them together. So...

(a^2/b)^-2 times (b^2/a)^-3

a^-4 / b^-2 times b^-6 / a^-3

Now you can't leave a number to the negative power. It must be simplified. Anything to the negative power equals 1/that number to the positive power. So...

a^-4 / b^-2 times b^-6 / a^-3

(1 / a^4)/(1 / b^2) times (1 / b^6)/(1 / a^3)

Here's me trying the sandwich method. Im not really fully understanding it but here's a try.

(1 / a^4)/(1 / b^2) times (1 / b^6)/(1 / a^3)

b^2 / a^4 times a^3 / b^6

Now, you cancel what you can.

The b^2 cancels out to 1, and b^4 is left on the bottom.

The a^3 cancels out to 1, and a is left on the bottom.

Now the simplified thing is 1 / ab^4

What I really dont get is all of the stuff for the sandwich method. Any body wanna try to explain that more to me? :)

This was probably the easiest week in the year so far. The thing that I liked so much is logs. Last year, ms. angie had us doing some crazy stuff with them and i could never understand them. But b-rob showed us how to do it.

Log 3 of 9 = 2

3^2=9

i thought this was so easy compared to what ms angie said...we had to change the base and all kinds of other stuff.

Log x of 81=2

x^2=81
x=9

Logs are now simple to me!

Reflection 5

This week went by pretty fast, as usual, and we learned quite a bit. The main highlight for this week to me are logs. i think they are simple and im glad i still remember them from algebra 2 last year

log4 of 16 =2
4^2 = 16

log x of 125 = 3
x^3 = 125
x = 5

Reflection 5

okay. So this week we learned alot about logs and stuff and we got taught how to sandwich. Thats something that actually confuses me and at the same time i dont see the point. I just flip it. But anyways. Logs are really easy most of the time. There are some certain exceptions to it. The only thing to really know is how to put them.

What you really need to know is if you have

log(x)2=9

x^2=9

x=3

its really simple. You cant really mess up on too much here.

reflection #5

this week we learned about logs

log 10x=a b^a=x

log (base 2)3=8; exponential form: 2^8=3

log (5)y=2 5^2=y

log (x)4=2 x^2=4 x=+/-2

Solving

log(2)16=x
2^x=16 x=4
log(2)16=4

10^x=75
log(10)75=x
log 75=1.875
10^1.875=75

exponential

f(x)=b^x | log or ln
D: (-infinity, infinity)| D: (0, infinity)
R: (0, infinity) | R: (-infinity, infinity)

i understand logs, but im having some trouble with the exponent problems

Reflection #5

This week wasn't that bad. The week went by pretty fast surprisingly, and the Chapter 4 test was pretty easy also. In class, we learned a lot about exponents and we started learning about logs and solving for them. I'm going to explain exponential problems, and give an example of one.

Example:

(b^2/a)^-2 times (a^2/b)^-3

For this problem, you have to distribute the ^-2 and ^-3 to both terms on their respective fractions. When there is an exponent inside parentheses, and another one outside, you multiply them together. When there is an exponent inside parentheses, and another one inside another parentheses, or both together, you add them together. So for this problem...

(b^2/a)^-2 times (a^2/b)^-3

b^-4 / a^-2 times a^-6 / b^-3

To further simplify this...

You cannot leave a number to the negative power. It must be simplified. Anything to the negative power equals 1/that number to the positive power. So...

b^-4 / a^-2 times a^-6 / b^-3

(1 / b^4)/(1 / a^2) times (1 / a^6)/(1 / b^3)

Now, to solve this, you can use the sandwich method. Here's how to do this.

You multiply the top and bottom terms, like the bread, then multiply the middle terms, like the meat, of a sandwich.

So...

(1 / b^4)/(1 / a^2) times (1 / a^6)/(1 / b^3)

a^2 / b^4 times b^3 / a^6

Now, you cancel what you can.

The a^2 cancels out to 1, and a^4 is left on the bottom.

The b^3 cancels out to 1, and b is left on the bottom.

So, the simplified fraction is...

1 / ba^4

Now, the only thing I didn't quite understand was the exponents and radical thing. with the fractions...would 2^2/3 simplify to the third root of 2^2, or 4?

Reflection #5

Okay, one thing I understand is logs:

To exponential form:
log(x)4=2
take the base (x), raise it to = ... (2), and set it equal to log of ... (4)
x^2=4
solve for x
x=+/- 2

To log form when base 10:
10^x=75
take number raised (10) and set as base, take the = ... (75) and set as log of ..., then take raised to ... (x) and set = to
log 75=x
then plug into calculator and solve for x
x=1.875

To natural log form:
e^x=75
put e as base of ln and put 75 as ln of ... then set x equal and solve for x by plugging into calculator
ln 75=x
x=4.317

Domain and Range:

Exponential:
D=(-infinity, infinity)
R=(o, infinity)

Log and ln:
D=(0, infinity)
R=(-infinity, infinity)


I do not understand the exponent stuff though. I know the basic rules, but when it comes to the actually problems such as ((1/x^2)^-1)^0 I just don't know what to do.
Anyone what to help?

REFLECTION #5

This week was alright. It went by really fast which was good. Monday we learned how to sketch graphs for different equations and Tuesday we reviewed all of Chapter 4. By Wednesday I completely understood everything we learned in Chapter 4 and the test was easy for me. The test wasn't as long as usual so I got to take my time on it and not have to rush through it, so I think I did pretty well on it.

On Thursday we learned about exponent rules and on Friday we learned logarithms. I thought that solving problems with exponent rules was simpler than logs so I'll explain that.

Here are some examples:

1.) 2^6 x 2^13 = ____ (multiplying)

*This exponent rule suggests that when the bases are the same (the bases are 2), you should add the exponents together.
then you would get>>> 2^19 and that simplifies to give you>>> 524,288

2.) 8^4/8^2 = ____ (division)

*For this problem, the bases are the same and it is division. When this happens, all you do is subtract your exponents..
then you would get>>> 8^2 which equals 64

**Those problems were pretty simple but what I thought was the easiest thing we learned this week was Solving for Exponents. To solve for an exponent, first you have to write your numbers as the same base. Then set the exponents equal and solve. Then you're done!!

Here are some examples:

1.) 9^4x = 81

*Okay, the first thing you want to do is make your bases the same number. (So ask yourself, "Can 9 go into 81 more than once?) yes, 9 can go into 81 twice.
So you would write>>> 9^4x = 9^2 (now the bases are the same)

So now you set your exponents equal and solve:
4x = 2
x/4 = 2/4 (divide)

x=1/2

2.) 8^x = 2^6

*Well this problem is a little different. Since you already have 2^6 you can see if you can use 2 as your other base for 8. 2 goes into 8 three times, so that would be 2^3.

Now your problem would look like this>>> 2^3x = 2^6
*Since your bases are the same, now you can set your exponents equal and solve for x.

3x = 6
x/3 = 6/3 (divide)

x = 2


***Alright, now for what I didn't quite grasp this week. I'm kinda having a little trouble with exponent problems that have addition in a fraction with negative exponents in it too. I do the first couple of things right but I get stuck towards the end so I probably end up making up my own rules for it. hah. *If anyone can explain it more for me that would be great :)

Overall, I thought this week was pretty good and I basically understood everything that was taught.