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