BOB on Exponents and Logarithms

Hey guys, please excuse this extremely out of place BOB-post! As some of you may know, I missed last week's test on Exponents and Logarithms and so my test is scheduled for tomorrow :].
I will try to make this BOB post substantial enough, but I don't know exactly how much I'm going to say so here I go!

Honestly, I think I'm going to find certain aspects of this unit test difficult! I've got the hang of everything we learned from the beginning of the unit up until the part when I left for the week. That means natural logarithms and the accounting portion will probably throw me off big time :/ Oh! And graphing logarithms... Ugh D: Nonetheless I will study hard!

Firstly, I must remember that a logarithm is an exponent! Don't forget!
This, as we all must know, is the basic form of an exponential equation:
On the other hand, the basic form of a logarithmic equation is:

In both cases;
a is the base
b is the exponent
c is the power

Now, there are several laws pertaining to logarithms. They are the Power, Product, Quotient, and Change of Base laws.
Power Law:Product Law:Quotient Law:Change of Base Law:
Ah, I almost forgot to mention that a logarithm is the inverse of an exponent! This comes in handy when dealing with graphing! We know that the exponential function results with the power when given an exponent. Therefore, a logarithmic function results in the exponent when given the base and power.

Alright, I can't quite say much about e other than I have noo idea what it is other than a "natural number" (?). I'm looking up websites and working on exercises as we speak! I will get the hang of thiiiis.

Also, we were given formulas pertaining to exponential/logarithmic growth and decay! Here they are, sadly though - they remind me a whole lot of Business class lol. Maybe that's a good, helpful thing?

PERT Formula:

Pe ^ rt = A

(for some weird reason the image maker won't allow me to have an exponent of rt :<)

P is the principle
e is the natural number
r is the rate
t is the amount of time
A is the total amount

MODEL Formula:

Ao is the original amount
m is the multiplying factor
t is the amount of time in total
p is the period of time it takes
A is the total amount

PERT's BROTHER Formula:

P(1+r/n) ^ tn = A
(again, some deal with the PERT formal, they really are brothers!)

P is the principle
1+r/n is the principle plus the rate over the number of times it is compounded a year (annually, biweekly, etc)
t is the amount of time

Okay! I think that's all about I can say... Of to study some more~
Wish us luck guys ;D!

Hello again Bob!!!

Hey everybody

Well this is probably the test I'm going to have the most trouble with because of the week of class that I missed because of the university thing. The unit seems pretty easy though and I'm fairly confident I understand what has happened since I've been missing so I will probably do alright. I am also now SOOOO thankful for both scribe posts and bobs because that is the only reason I understand what I do. The only thing I'm really worried about is word problems because I wasn't in class to learn how to do them. Well there's not much else I can say that hasn't already been said so I'll see everyone tomorrow. Bye.

An Exponentially Exhausted BOB!

LOL. Yes this BOB maker is exponentially exhausted. The number of activities I had exponentially grew and my energy exponentially decayed. xD Anywho, here's my BOB post.

This unit, Exponents and Logarithms, started off very easy for me. But of course, back then, we were just starting off reviewing some of the basics such as the "anatomy of a power" and rewriting numbers as powers and vice versa. We were also doing some simple equation solving with them which also came quite easy to me.

When logarithms were introduced, I'll have to admit, I was pretty worried because it seemed very confusing but it was actually straight forward. Although I almost never forgot, it took me a few days to grasp the concept that "A Logarithm is an Exponent!" [and you're gonna forget that! (the wise, wise words of Mr.K) :D]. Once I did get that concept, I felt a little bit more relieved about the logarithm part of the unit. The equation solving also came relatively easy to me.

I would have to say the hardest part of the unit was when the compound interest stuff showed up. I guess it was because at first, I had a bit of a hard time understanding it, but it's sort of clear now. However, when it got combined with the concept of "e" that's where I got lost. Me missing a week of school didn't help that too much but luckily us university goers worked together to try to piece together information from the scribe posts and from the slide shows (BTW thanks for the scribe posts guys! It really helped.). However there were some things that still needed to be cleared up(such as the word problem stuff that was covered while we were away) and that was cleared up through our visit to Mr.K on Friday (Thanks Mr.K!).

Well now that I've covered what I thought of the unit, what was hard and what was easy, I guess it's advice time! Well there's really no sense in giving advice now when the majority of the class has already written the test but I'll mention the important parts anyways in hopes that this will miraculously stick to my brain.

1. A LOGARITHM is an EXPONENT.
2. a^b=c can be rewritten as loga(c)=b to find the exponent
3. Product law (log MN= log M + log N)
   Quotient Law (log M/N= log M-logN)
   Power law (log M^N=Nlog (M))
   and the Change of Base law (log a(b)= logc (b)/logc (a) )
4. Remember the exponential modelling equations (like A=Pe^(rt))
5. "ln" is the same as log e

What else can I say? Eat, sleep, study, yenno the normal test routine.

Hmm.....I know I'm missing something.......ahhh, yes.

I think that I will do well on the test. I'm not too confident however because of the week of class that I missed. Do I regret doing that? Well, yes because I feel like I've missed a lot in my classes (especially math at the moment) but at the same time no because then I would've missed out on such an amazing experience with some amazing people! Hopefully I do well on the test and I don't forget anything (please let there be a formula sheet -_-", if there isn't that's fine too).

Good luck to my fellow classmates who are going to take the test and to those who have, it'll be nice to be back in class again.

~jayp~

P.S. A LOGARITHM IS AN EXPONENT!!!! lol.

BOBlog

Good Morning bloggers! I could not sleep so what better time to do my blogging on blog post! :)

This unit was exponents and logarithms. It started of as a scary subject but as it went on I did not find it terribly difficult and understood things quite well and quickly.  Time for a review!

Alright, first thing to say is that a logarithm is an exponent!!!! I have not forgotten that yet and I don't plan on it!!!

The basic form an exponential equation is A^B=C where A is the base, B is the exponent and C is the power. Ex. 95^2=9025....... (It's over 9000!!!!! XD sorry for that)

The basic form for a logarithmic equation is logAC=B where A is the base, C is the power and B is the exponent. 

A logarithm is the inverse of the exponential function. For the exponential function you "feed it" exponents and it gives you powers where as a logarithmic function you "feed it" power and it gives you exponents. (I'm really tempted to make more over 9000 references XD)

Now there are several laws when working with logarithms you should know. There is the Product law, Quotient law, Power law, and Change of Base law.

Product law: loga(MN)=logaM+logaN 

Quotient law:loga(M/N)=logaM-logaN

Power law:loga(M^N)=NlogaM

COB law:logN(M)=loga(M)/loga(N)

There is also the mystic and all powerful number e!! Check out the history of it here!! Anywho... Using the number we we can make The exponential function and The logarithmic function, being f(x)=e^x and f(x)=ln(x) respectively. (ln is the same as loge)

Woah! Almost forgot but there is some things on exponential growth and decay as well! Now if I remember correctly we can use the Pert formula of A=Pe^rt where A is equal to the final amount, P is what you start with, e is e, r is the rate and t is time in years. With this little bad boy of an equation we can solve INTERESTing problems.....XD.... as well as we can calculate half lives with it. If all else fails you can whip out A=P(1+r/n)^tn where n is the number of times we compound the principle value per year. As a side note, if you take 1 dollar and compound interest on it at 100% for a year and you did it enough times, like more than once per second it would eventually plateau out at number e!

One more thing, I remember Mr K. going over those modeling questions there are 2 formulas for that!! A=AO(model)^t where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, the model is how much it has either grown or decayed and t is the time that has passed. This is used when you have minimal information.

If you have a lot of info then you may use A=AO(m)^t/p where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, m is the growth rate, p is the time required to multiply by m once and t is equal to time.

Well i think that about raps it up. I am off to sleep because I am exhausted.

BOB was sitting on a LOG...

Anyways, this is my BOB, and no I am not late since i didn't do my test yet.

Since I missed a whole week I have a feeling that all those word problems and questions involving e will be my downfall since that is what the class covered while I was away. Just saying.

Here is stuff that I should remember for the test:

a) A LOGARITHM IS AN EXPONENT.

b) When solving exponential equations, make sure the base is the same. If the base is not the same use log.

c)When dealing with quadratics, reject the negative answer since it will make the log/exponential function undefined.

d)Know how to draw these functions and describe them (range, domain, increasing/decreasing etc.)

e)Know the laws:
i) The product law
ii) The quotient law
iii) The power law
iv) The change of base law

f) Know the formulas, unless Mr. K is nice enough to have a formula sheet :D
i) A=P(1+r/n)^(t*n)
ii) A=Pe^rt
iii) The rule of 72 ?
iv)A=Ao(model)^t

g) Just know that ln is the natural logarithm.

Alright. I guess that's it... just eat, sleep and study right....

May I request that I do my test wednesday Mr. K? :)

B0B

Hey, here is my bob for the exponents and logarithms unit.

I was at the U of W for last week so I missed a lot of stuff, but after reading over the slides and doing the homework I think I have a grasp on what I'm doing.

Some things that I think will be important for the test are:

A logarithm is an exponent!

That means that when you are multiplying 2 logarithms (logMN) it is the same as adding them! (logM + logN) This is known as the product law.

When dividing 2 logarithms (logM/N) it is the same as subtracting them! (logM - logN) This is known as the quotient law.

When you have an exponent (logM^N) it is the same as multiplying (NlogM) This is known as the power law.

It would also be handy to remember the change of base law. This means that when you want to change the base of log all you have to do is divide log the base you have by log the base you want. (If that makes sense? It helps me to think of it that way)

Also know the equations for finding interest A= Pe^rt. (this also works for decaying questions or for finding the half life!)
A is the end amount. P is the amount you start with. r is the rate. t is the time in years.

This equation is handy for word problems, but if it doesn't work there is always A= P(1+r/n)^tn
where n is the number of times the principle is compunded per year.

ln is the natural logarithm, it is the same as log base e, but we never write this! Just write ln! We can use ln the exact same way we use log!

Well those are the things that I discovered from doing the homework. I think that pretty much sums up the unit.

I think the hardest part of this test will be remembering the word problems because I wasn't in class to learn what not to do. Hopefully my day of studying will pay off though because I feel like I really understand this unit! (:

BOB

Hi, this is Alex doing my BOB 10 minutes before the test. I feel like I have a general understanding of the topic of logarithims etc. Unfortunately, I don't feel ready. I haven't had any time to do my homework and I haven't had any time to study. I'm just going to wing the test and hope what I learned in class was enough.

Good Luck to everybody. Hope you do WonderfullyExcelent!

BOB

hi everyone, this is aldrin b.

well, i don't have much to say because
i'm still having trouble regarding this unit so,
i just want to wish you all luck for this exam.

just remember,

~A LOGARITHM IS AN EXPONENT~

BOB

Just remember that have to bob
I was still studying!!!! hard !!!!!!!
I didn't get the last part, don't know which formula should use for which question.
Still trying to went over my notes and find out.
Well any way!!!!!! Good luck everyone have a good mark.

BOB

hi, this is Ale
Today is a test and i hope every one of us is preparing himself for the morning test. a lot have been reminded by our dear classmate but i also want to remind you two thing adding on what our friend have already said.

1. don't forget to write your answers in 4 decimal places
   
2. when using a calculator in order to be accurate remember to store your answers in Alpha A
   

Good luck everyone and lets hope the test will be done in a good condition and everyone will finish it smiling

MY LAST MINUTE SUPER SPECIAL AWESOME ULTRA SUPER BOB!

Haha hey folks. A little late but here goes!

A logarithm is an exponent. 'Nuff said! Mr. K says we're going to forget. So don't.

My personal reflection:

This unit was pretty straight forward. Ln is the natural logarithm in base "e" (Euler, a big hero of Mr. K) was something cool i learned because I always wondered what it stood for on my calculator.

I was sad :( that I had to leave our workshop early today but my teeth are getting fixed so i guess it all balances out! Or maybe not... anyways I believe I am very prepared for the test tomorrow but I'll probably be really tired so hopefully that doesn't make me bomb during the test.

Important points:
~ STUDY
~SLEEP
~EAT
~SLEEP
~STUDY
~SLEEP
~HOPEFULLY YOU'VE ALL DONE YOUR HOMEWORK!! =D

Anyways yeah I'm really dead... for those who haven't seen "The Wiz" yet... you totally should come see it tomorrow! Doors open at 7:00 pm and tix are 7 bucks! Anyways I'm off to bed but good luck 2morro everyone! NIGHT!

OMG BOB!

WOW almost forgot about bob. So this will also be short since its really late xD. I'm probably not very confident because I haven't really practised so much on exponential functions. I may have problems understanding some of the word problems and how I need to approach such a problem.

I will probably not have enough sleep since I've got other things to do. Might not be prepared. So I'm actually frightened about the test later today because I'm probably going to fail. I will try to study if I can. Otherwise my best luck will be making myself a nice big breakfast so I have some energy to do the test :D.

I've learned alot about logarithms but exponential functions I will have to look into.

That's about all I have to talk about. Also I give the same old advice to everyone EAT , SLEEP and STUDY. And yes I know I'm not goign to follow my own advice, but thats why I'm probably goign to fail. GL TO EVERYONE! HOPE YOU DO MUCH BETTEr THEN ME! xD

BOB

(I just realized that I'm a visual learner! The youtube videos embedded in the slides help me big time. ^^)

Okay, so here we are, finishing another unit of our course, entitled EXPONENTS and LOGARITHMS. I liked this unit because it has laws and formulas that we use as tools to solve a problem. Speaking of formulas, that's where I had problems with. I didn't know what formula to use in exponential modeling because there were many that we learned. But I think I get it now. Hopefully I won't get mental block tomorrow.

Good luck to all!

BoB Exponents and Logarithms

Bonjour! It's kalekalekale here just gonna do a quick BoB and get to studying after a long day of work. This unit was very informative and fairly straight forward. I found myself lost in this last week because of the fact that I missed class on monday. Thanks to you wonderful bloggers, I'm back on track. Well, we have a test tomorrow and I hope everyone studies.

Don't Forget:
LOGARITHMS ARE EXPONENTS

B to the O to the B, BOB

So I almost for got to do this. I have been neglecting my homework for this unit, well because I have some very important studying to be done (just a week and some left) and major projects to be finish. With that said I did not get as much practice as I wanted, so I'm afraid for the test. I really do hope that I'll do well but lets just see how things go. I'm gonna go back to do what I was doing prior to this now and I'll be stuDYING . Well good luck guys and break a nail.

A LOGARITHM IS AN EXPONENT!!!!

BOB

Alright, I practically have no time to provide this BOB with any mathematical help. I'm confident about this unit as well. However I must complete my super important English assignment asap. I suggest looking at the slides, doing homework, MENTALLY REVIEW (without paper), and increasing your confidence by means of saying stuff like "im gonna rock this test!" And you do not have to say that stuff, but like just believe that youre gonna smoke the test because it is helpful. Good luck everyone!!

IS YOUR DELICIOUS LINK HERE ??
HERE!!!!

Exponential BOBs

Well seeing as the test is coming up tommorow and everyone is scrambling to do their posts, I guess i's my turn to do mine.

This basically this test is gonna be about logrithims, so all we need to remeber that logs are exponents.

If you have log(MN), you could express it as log(M) + log (N)
If you have log(M/N), you could express it as log(M) - log (N)

And you can remember Pert and what not, and the reason we like to use "e" is because the exponent is the rate.

So thats's basically what i think i need to remember, so good luck on the test tommorow guys and gals.

BOB for Exponents and Logarithm

About this unit, i think there are some thing that we need to remember:

- A LOGARITHM IS AN EXPONENT. (Mr.K always says that we're going to forget that!!)

- The product law : log_bAB = log_bA + log_bB


- The quotient law : log_bA/B = log_bA - log_bB

- The power law : log_bC^k = k(log_bC)


- The change of base law:

- The exponential function : f(x) = e^x


- The natural logarithm : f(x) = ln(x)


About the formulas:

- A = P(1+r/n)^tn

- A = Pe<sup>rt

-</sup> A = A₀(m)<sup>t

-</sup> A = A₀(m)<sup>t/p

I wasn't in class for a last few days so i'm not sure if this is enough, but i think i kind of get it now even though i got some confused at first. Anyway, GOOD LUCK to every one. ^^</sup>

Reflection

Big Ups to Anthony!

He's been a trooper helping me out :D also my late night study budy. HAHA seriously guys, ADD ME :)

So far so good. Not an overly difficult topic but because I haven't been practising.. I haven't gotten it down pat yet!

It's pretty much embedded in my head that:

• A logarithm is an exponent!

Short and sweeet. Just like me :)
(Note to self: never say that agian)

Time to study!

---------

Okay, maybe it was TOO SHORT.

Since I haven't been attending class lately, I've been relying on the slides and on your scribe posts!

I say, GOOD JOB! It's been helping me ALOT :)

Helpful hints:

• don't forget a logarithm is an exponent (this was a little difficult to understand in the begning)
• factor (it's so much easier to solve logarithms after factoring .. PROPERLY)
• log and ln exist on a calculator for a reason :D (i just learned that @1am)

There are a few things thought that I've been having trouble with since some of the slides do not explain EVERYTHING.

Such as: (being that {x} = subscript)

• a^x = b turns into log{a}b = log{c}b / log {c}a
• log{5}( 3x + 1 ) + log{5}(x-1) = 3 turns into 3x^2 - 2x - 1 where did the log{5} go?! and why!?
• reason for rejecting?
• antilogs
• ln is confusing
  

Note to self: Study earlier. (Yes, it has taken me this long to realise :) haha)

" You only fail when you've given up completely. "

BOB

So, tomorrow is our test, and after reading over our slides over and over again a few days ago, I finally get this unit! Yes, I finally get this unit.

At first, I really really disliked this unit, jut because of the fact that I didn't like exponents. Yes, I know what you're thinking, "Who doesn't like exponents??" Well, i did. I didn't get how negative exponents worked, and now after reading over the stuff, and after I gave it a try, well.. I realized that it wasn't that hard to understand.

There aren't really a lot of things to remember for this unit, except for the fact that A LOGARITHM is an EXPONENT. Another thing to remember would be that an exponential function turns an exponent into a power, while a logarithmic function turns a power into an exponent.

These are the laws that we should know:

The Product Law
log_bMN = log_bM + log_bN

The Quotient Law
log_{b(M/N) =} log_{bM -} log<sub>bN

The Power Law</sub>
log_bM^k = klog_bM

We should also know that when no base is indicated, the base of the logarithm is base 10 .
Also, remember the
Change of base formula:


some formula's we should know about..
A = P(1+r/n)^t
A = Pe^rt

A = A₀(model)^t
A = A₀(m)^t/p


Well, yeah, that`s pretty much what we`ve learned in this unit. There are a few more, but I can`t really remember them at the moment. So I guess I`m off to study.