Exponents and Logarithms worksheet

Here is another comment regarding Zeph's questions. I really enjoy answering questions. It sorts of review me about everything i learned last year.


Zeph,

Now I'm going to show you how to do question 16. Special credits to benofschool for showing me how to do this.

[log_3(X)]^2 - log_3(x)^2 = 3

Apply the rules of logarithms.

[log_3(x)]^2 - 2log_3(x) = 3

Let, log_3(x)= y

y^2-2y=3

Apply algebraic massage

y^2-2y-3=0

Solve for y.

(y+1) (y-3)=0

y=-1 y=3

Substitute back log_3(x)= y

log_3(x)=-1 and log_3(x)=3

x= 1/3 and 27

I'm going to post the answer for the other questions tomorrow.

-m@rk

Exponents and Logarithms worksheet

This was my answer regarding Zeph's question. He was asking on how to do a specific question because he was not in class for the whole week because of some extra curricular activity. Here it is.


Zeph,

I'm going to answer your second question first, since it is tougher.

Question 15

logX^2 = (logX)^2

First is to apply the rules for logarithms.The equation will look like this:

2logX= (logX)^2

Now, let logX= y (or some other variable. The equation will look like this:

2y=y^2

Do some algebraic massage

0=2y-y^2

0= y (2-y)

y= 0 and y=2

Now substitute back logX=y

logX=0 and logX=2

Take antilog of both sides

x=10^0 and x=10^2

x=1 and x=100

-m@rk

BOB Version 4: Exponents and Logarithms

This was my comment on Zeph's BOB post. I've finally caught up on my mentoring duties. Again, I apologize, If I'm doing my comments a little late, It is just because that AP exams are just around the corner and its almost crunch time.

Zeph,

Good BOB post! It seems to me that this new format is going to attract more attention. There are more people who are going to imitate this, much like your other format. Over my two years with Mr. K, I've never seen this done before. You are continually proving that math coexist with language. Good luck on the upcoming test.

-m@rk

BOB for Logs

This was the comment I left on Rence's BOB post. It is interesting to see how they are improving as time passes by. This bunch of people are continuing to intrigue me, now I cant wait till Ap exams are over , so i can do some math with this people.

Rence,

I hope that you study hard for the upcoming test.On your BOB post, you mentioned, "Ln (pronounced Ellen..). Apparently it's easier BECAUSE it has ONE LESS LETTER." A clever reason but that is not the case, if you want to know why Ln is widely easier, I think that you should take AP Calculus for next year. You will see that the base e has so many cool properties. I don't want to spoil anything, so I'm going to stop now. Good luck!

-m@rk

"EXPONENTIAL MODELING"

Now that the AP exams is only about three weeks away, I'm starting to forget about my mentoring duties, my apologies. This was my comment on Jamie's scribe post regarding exponential modeling.
Now i just need to do more catching up.

Jamie/PBnJamieSnagwich,

Good scribe post.I like how you modified Zeph's format and you said that "I'm not the one who follows the whole OUTLINE idea, because not everything I write is written in stone". Thats a good move, because not everyone works the same way. People have their own different ways of expressing themselves.

-m@rk

Logarithms and Exponents Practice

After reading some people's reflection on the logarithms and exponents unit, I must say that they are pretty comfortable with the concepts, but i still decided to make a post containing some of the online quizzes that they can use to study and ace the test tomorrow.

I can see that most of you guys are loving this unit, but I still made a collection of online quizzes that can be found around the net.There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

Link 1
Link 2
Link 3
Link 4
Link 5
Link 6
Link 7
Link 8
Link 9
Link 10

I planned to post this earlier but my internet connection is acting weird because of the weather outside.

-m@rk

Logarithms and Their Laws

This is comment on Joyce's post. Her post was also about logarithmic laws and its application. I must say that I'm loving how they are including images when they are trying to explain a certain concept. It is just easier to learn compare to a scribe post with just plain text.

Joyce,

I must say that it was a really long scribe post, but it was very well done. Like i said on Kristina's scribe post, I like how you inserted an image so that your readers can easily link to what you are saying. It saves them lots of time and most of all makes them learn visually. I like to consider myself as a visual learner so this post really helped me relearn all this laws.

-m@rk

Logarithmic Laws

This is my comment on Kristina's scribe post. Her scribe post was all about logarithmic laws and its applications, so without further ado here it is.

Kristina,

I personally like how you included an image when you were trying to explain the logarithmic laws. It was easier to understand and it save me lots of time because i don't need to scroll back and forth from the slides to your post. Now, i need to relearn all this laws once again.

-m@rk

Logarithmic Spiral

Well, after one of the busiest week of my life, this was the only time that I've finally caught up on my mentoring duties and reading, so here was my comment on Richard's scribe post titled "Logarithmic Spiral".

Richard,

Good scribe post. I learned a couple of things from your post. First, I didn't know that snail shells, tornado , spiral galaxies and even Romanesque broccoli grows the same way as the logarithmic spiral. Second, i need to do 2 quizzes tomorrow. Lastly, just a word of advice, you might want to highlight some parts of your scribe post if you are trying to emphasize an important concept.

-m@rk

Solving Exponential Equations + Looking at exponential graphs.

Well, i thought that I would drop by and leave Eleven's post a comment. The post itself was kind of late, because the last time i checked at about 2:00 am , it was not yet published, so without further ado here is my comment.


Eleven,

Its better late than never, eh? Well, I personally like how you structured your scribe post, especially the little side comments at the end of each question and how you use bold letters to emphasize a certain concept. Those are good methods to make the concepts stick in your head. It seems to me that you are really comfortable in what you are doing. Good job!

-m@rk

FLick Off

Well, now that I'm on top of my todo list (thanks to the week long break). I decided to continue my mentoring chore, so this was my comment on PBnJamieSnagwich's post.

PBnJamieSnagwich,

I'm sure that Mr. K will look at your suggestion of grouping all your flickr photos into just one place so it can be accessible in just one click. This ca be very useful if you want to use the flickr images to study. I really think that it is a clever idea.

BTW, I watched the movie, 21 too. I really think that it was very clever, but i don't recommend that you guys should go gambling. I wonder if Mr. K will use the movie when you guys study the unit of probability.

-m@rk

Sum and difference identities

This was my comment concerning this specific identity. I personally detest long formulas but this one is very useful and easy to remember.

A very well detailed scribe post. This scribe post helped me remember the concept behind this specific identity. I remember the fist time that i learned this identity, i found it really dry and boring. Now, i just need to put this found knowledge in the upcoming test. Keep up the good work!

-m@rk

Also, another comment concerning the same matter.

Anhthi,

Good scribe post. This scribe post sort of reminded me of the JABBAWOCKEEZ because of the way that you use kinesthetics to learn the sum and difference identities. Next year, if you take Calculus with Mr. K you guys will not just dance but also sing. Also, about that superstition about writing your name in red ink, my friend said that it doesn't mean anything important. Keep up the good work!

-m@rk

Just a little help...

I remember when i made this post i was going over their BOBs and i was starting to see the same pattern that everyone still need a little bit of practice about trigonometric identities for the upcoming test.

I can see that most of you guys are having some trouble with trigonometric identities. The only way that you can be good at it is by doing some practice questions, so you can develop a knack on seeing the patterns in this mini mind puzzles. There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

http://library.thinkquest.org/20991/alg2/trigi.html#Quiz
http://www.syvum.com/cgi/online/serve.cgi/math/trigo/trig2.tdf?0
http://www.quia.com/cc/448321.html
http://www.epcc.edu/Student/Tutorial/Mathcenter/Exams/trigquizzes/quiz14/QUIZ14.htm
http://www.libraryofmath.com/trigonometric-identities-quiz.html
http://www.batesville.k12.in.us/physics/CalcNet/Trig_Review/Trig_Review.html
http://college.hmco.com/cgi-bin/SaCGI.cgi/ace1app.cgi?FNC=AcePresent__Apresent_html___mathematics_larson_algebra_trig_6e_07-02

-m@rk

Pythagorean Identitties

This is my comment to Zeph. I was clearly intrigue by the format of his scribe. I wish my mind works sequentially and clearly as his post.

Zeph,

I should say that I'm really impressed by this post. This post is very well written and organized. I like how you make outlines, it sort of summarized everything that happened in class. Keep up the good work!

-m@rk

Word problems

I know that i should have posted this a long time ago, but this past month has been a killer for me. Well, it was a good test of time management and mental toughness though so without further ado, here's one of the comments i made a month ago:

After doing the whole question by myself, I must say that this is the most challenging question among the bunch. It took me about 35 minutes and a lot of coffee. I think that you have the arrow of the wave on the left of the x-axis on the right position contrary to what other people say. Good luck on the upcoming test.

-m@rk

Also, i made another comment on the same assignment from a different group:

Paul,

I think you made a good point. I also think that the amplitude should be 20 because the ferris wheel is 1 meter above the ground.That being said the vertical shift will change too,it will be 21. Like you said it is a matter of one's interpretation. Now, i kinda like to go to class once in a while to see the class's progress but too bad i still have my AP class.

-m@rk