Precal Blog

Hey everybody!  So we have our mid-quarter test on Tuesday, so it’s time to review everything we’ve covered so far this quarter!  Mr Bieniek was gone most of the week, but he did give us a list of the nine LTs for the test.  We spent Friday in class reviewing the LTs with at least one question per LT.  I guess I’ll post those questions (or the general idea of them) for the LTs we covered for those of you who weren’t there or didn’t copy them down – you can check out the problems and see which ones you need some work on, then think of some questions you could ask Mr B on Monday. 

LT#1) I can explain how the values of a and b affect the graphs of exponential functions.

For this LT, check out your notes from the first packet (A-1 on the yellow sheets) or your notes form January 23rd.  Basically, there are four forms an exponential equation can exhibit: concave up and approaching zero (from left to right), concave up and getting further from zero, concave down and approaching zero, or concave down and getting further from zero.  A can either be more than or less than zero – it can never be equal to zero.  B can either be greater than one or inbetween one and zero.

 LT#2) I can apply the concepts of exponential functions to a real-world situation.

For this LT, look at the exercises in packet A-1, especially at the problems about the bank or deer population, etc.

LT#3) I can recognize an exponential function from its numerical pattern in a table and write an equation for it.

Problem:  If f(2)=7 and f(5)=21, find f(14) and write an exponential equation for the values. 

Solution:  If you make a table of values, you will see that each time you add three in the x-values, you multiply by three in the y-values.  Therefor, b(intervals of 3) is`21/7`.  This means that something multiplied by itself three times is equal to `21/7` or three.  That means that b(intervals of 1) must be the cubed root of three.  Insert that value into an equation to get a.  For example, 7=a x the cubed root of three squared, a=7/cubed root of three squared.  To find f(14) just insert 14 in for f(x) in your equation with the values of a and be that you found.

LT#4) I can interpret logarithms as distances.

LT#5) I can estimate (with good accuracy) the values of logarithms by using the three properties of logs.

I’m just going to list the three general rules for logs – if you need practice, look at the exercises on pg 108 of packet A-2 or the notes from February 4th.

1. log(ab)=log(a)+log(b)
2. log(b/a)=log(b)-log(a)
3. log(a^n)=nlog(a)

LT#6) I understand how to convert logarithms from one base to another.

For practice, Mr. B gave the problem log-base7 of 63.  Check out packet three if you need a how-to on base conversions.  I’m not so great at this yet, so I don’t want to give you the wrong info!

LT#7) I can solve logarithmic and exponential equations. 

For practice, look at the worksheet Mr. B gave us on Feb 13th.  Again, I’m not so great at this yet!

I know this post is really long and might be hard to follow.  If you don’t get it, just look through your packets really thoroughly and any class notes we took.  If anyone can explain it better, please comment or post!!!  See everyone on Monday!  And don’t forget to think of any questions you might have for Mr. B  or the class

Lindsay;)

P.S.  If anyone else is addicted to Sudoku or Yubotu, I found a great site with a ton of logic games!  Here’s the link: http://www.dkmsoftware.com/PlayOnline.htm

As the title states, I guess I’ll just blog about the last 3 days in Precal, since I don’t know if I’m supposed to do it or whatever.  Well, pretty simple, we got a new packet to work on in class with our groups.  Work out the activities, conquer the exercises.  You know the drill.  And if you seem to be getting stuck on this current stuff on logarithms, really seriously read the packets!!!!  They work out wonderfully.  I found out that after reading the packets over once or twice more, I understood the concepts.  I hope it’s the same for you!  See ya’ll later, I’m goin to Florida tomorrow ’til March 1st!  

Hey guys, this is blogarithm the prequel because 1. this was supposed to come a day before saywer’s post and 2. because i came up with the name blogarithm and sawyer does not deserve credit for it. (patent pending) On Monday the whole class was pretty flummoxed at the new packet we got. It started to deal with logarithms in a somewhat different way that a lot of us were having a problem understanding. It focused on putting logarightms into a physical perspective as we used different base scales and compared them to other base scales. It was very interesting to see how they related and how each one could be changed to the other.

If you want to hear more please tune into 102.9 the BLOG lol

Okay guys well i gotta go watch my favorite movie…Blogma.

alright im done now. sorry about that.

This is my blog for Friday the 13th.

Its bad luck to blog on friday the 13th so im doing it now.

On friday we recieved a worksheet which i left in my locker over the long weekend so i can’t give examples. What the ws dealt with was using the log properties to solve various log equations. If the equation couldn’t be solved with out a calculator, using the log properties, we manipulated the equation to include log base 10 or natural log so we could simply solve it with our calculators.

hola everyone this is from the 10th. My computer has been on the fritz because of some power grid problem in my hood so sorry its a lil late.

so on tuesday we looked at the packet 2-3. and tried to do problems 1-4.

problems 1 and 2 had to deal wit graphs so im not gonna post that. 3, however, i will.

So for 3 basically we were trying to figure out a ratio between base 2 and base 10 logs. the conclusion we came up with was to convert from base 10 to base 2 you do the base10log of the power number divided by log2. To go from 2 to 10 you do the base2log of the power number multiplied by log2. all this means is that the exponents in base 2 and 10 have a ratio of log2.

Once again sorry for the tardyness of the post. Hope this helped a little.

Today in class we talked about converting from one log base to another. We decided that to do this, you must find how many units of one log base fit into another log base; and with that, you can multiply your given log to find the log of another base. For instance, we found that:

log₇(x) = log₅(x) * log₅(5)/log₅(7)

and

log₅(x) = log₇(x) * log₇(7)/log₇(5)

Then, Mr. B gave us a problem in which we were supposed to use the same techniques as shown above (converting between different log bases). Some students used this method, but I don’t fully understand it; so instead, I used the log rules that if y = log_bx, then b^y = x  and log_b(mⁿ) = nlog_b(m). The problem given to us was to convert log₂(13) to the log base-10 scale. To do this, I did the following:

log₂(13) = x

2^x = 13

log(2^x) = log(13)

xlog(2) = log (13)

x = log(13)/log(2)

And that’s the Brandon Method. My solution is equal to the one the rest of the class got when using the other method:

log₂(13) = log₁₀(13) * log₁₀(10)/log₁₀(2)

and because log₁₀(10) = 1,

log₂(13) = log₁₀(13)/log₁₀(2) = log(13)/log(2)

Both methods work and get the same answer. I like the Brandon Method though.

Wow guys, sorry this is so late!

Well, on Thursday we had a presentation called “Can I Kiss You”  during first hour classes.  Which left 3rd hour with only a 35 minute class.  On top of that we had activity pictures.  So honestly I’m not sure of what all went on in class seeing as I was gone most of the time for pictures.  But I’m sure we just worked on our Log packets.  So nothing too interesting happened on Thursday.

Have a nice week everyone!!!  =]

So today we had an assembly. Third hour only had a 35 min period, but 5th hour had an hour! Today all we did was continue to work on our current packet. Claims will be coming soon!! Just keep working on the packet!

I worte this blog entry on February 2nd but for some reason it never showed up.  I waited a little bit to see if it would but it never did, so here I’m going to repost it:

Today we began the class by quickly going over what we did independently in the packet for logarithms.  We should understand logarithms, such as the log of 100 is 2 because 100=`10^2` and the log is the power of 10.  We said that on a number line of logs from 1 to 10 the magnitute between each integer increases as we get closer to 10 because the difference between `10^2` and `10^3` is less than the difference between `10^3` and `10^4` and so on.  Next, we worked on Activity 2.4 (Page 102 in our packet).  We worked on this for the whole class period and for homework we should get through #2 and read and be ready to work on #3 for tomorrow.