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

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

Critical Thinking

While I was surfing through the blog, I noticed that most of the post were talking about Mr. K's new gimmick of making his students think. His new gimmick is to tell one lie per day so that his students will critically analyze everything that he says. This method sorta reminds me of this blog post that i read on one of the blogs on my rss feeds. The post talks about another teacher that uses the same methodology to make his students pay more close attention to what he is saying.

Zeph,

I'm quite impress that you caught that lie. I didn't even caught that one when i was trying to redo the whole question by myself. It's quite nice to see that many of you guys are getting a lot from Mr. K's lies. I guess that his strategy makes all of you critical analyze what he is saying.Good job and keep up the good work!

-m@rk

Tangent Function

Second post on my mentoring blog.While I was doing my regular routine of reading our blog the most common thing that i see people have problems with is the,tangent function. Anyways,what is the tangent function? It's time to put my thinking cap on and help my fellow classmates with this.


Zeph,

As for your other question. The graph of the tangent function can be viewed here: http://fooplot.com/index.php?q0=tan(x)

The tangent function has some cool properties. It has an amplitude of undefined, a period of pi and y intercept of zero.

I have so much more to say but i don`t want to spoil the fun.

-mark

Also, I've seen a similar question from Roxanne, so i decided to give her some insights about the tangent function. I gave her more details.


Roxanne,

If you want to see the graph of the tangent function, you can go right ahead and use fooplot.com. You will see that the shape of the tangent function is somewhat different from cosine and sine.

The graph of the tangent function has some distinct properties.It has a period of pi unlike both cosine and sine which has a period of 2pi.
Second, it has a y-intercept of zero. (There are so much more to say about this function but i wont go into them, because i don't want to spoil the fun).

Graphing the tangent function follows the same rule as graphing both cosine and sine functions. The general equation for the tangent function is f(x) = a*tan(bx+c)+d. You can see that it uses the same parameters.All the parameters work the same way as the one in the sine and cosine equations. It also follows the same algorithm DABC (but i prefer using BCDA).

I hope this helps you clarify things.

-m@rk

Function Notation

First post on my mentoring blog. Kind of weird trying to help my fellow classmates in their math studies based on my experiences and wisdom that I gained from taking this class last year.


Zeph,

Question #15 on exercise 2 is just simply using function notation. Since f (x) = 2x + 3 and you have to find k so that f(k+2) = k + f(k).
so we`ll work on the right side first, all you have to do is just substitute k+2 to x so you have:
2(k+2) + 3

On the other side since k is just a constant you just leave it and then again reading the function notation you need to substitute k to x so you have this:
k+ 2(K)+3

Therefore, you will end up with this kind of equation:
2(k+2) + 3 = k + 2k + 3

Then with the help of some algebra you will get this answer:
2k + 7 = 3k + 3
4 = k

-mark