Logarithm

Task 1

A to the power of m times a to the power of n equals a to the power of m plus n in bracket. A to the power of m over a to the power of n equals a to the power of m minus in bracket. Logarithm b to the base a equals n, so b equals a to the power of n. logarithm a to the base g equals x, a equals g to the power of x. logarithm b to the base g equals y, so b equals g to the power of y. What about of logarithm a times b in bracket to the base g??? Answer:

1. Logarithm a to the base g equals x, so a equals g to the power x.

2. Logarithm b to the base g equals y, so b equals g to the power.

3. a times b equals g to the power x times g to the power y.

4. a times b equals g to the power x plus y in bracket.

5. Logarithm a times b in bracket to the base g equals x plus y in bracket Logarithm g to the base g. (Logarithm g to the base g equals one)

6. So, Logarithm a times b in bracket to the base g equals Logarithm a to the base g plus Logarithm b to the base g

a over b equals g to the power x over g to the power y. a over b equals g to the power x minus y in bracket. Logarithm a over b the base g equals Logarithm g to the power x minus y in bracket.

Task 2

Equation :

1. a x to the power two plus b x plus c equals 0.

2. a x to the power two plus b x equals minus c

3. x to the power two plus b over a x equals minus c over a

4. x to the power two plus b over a x plus b over two times a in bracket to the power two equals minus c over a plus b over two times a in bracket to the power two ( plus b over a x plus b over two times a in bracket to the power two both internode)

5. x plus b over two times a in bracket to the power two equals b to the power two minus four times a times c all over four times a to the power two.

6. X plus b over two times b equals plus minus root square of b to the power two minus four times a times c all over four times a to the power two in bracket.

7. X plus b over two times b equals plus minus root square of b to the power two minus four times a times c in bracket all over two times a.

8. X one or x two equals open bracket minus b plus minus root square of b to the power two minus four times a times c close bracket all over two times a.

9. If a x to the power two plus b x plus c equals 0, so a, b, c, part or number Real and not zero.

It Is a Must that I Have a Competent in English for Mathematics Education

The ability to speak English is one of the very ability to determine the gain in employment of late. This is the phenomenon that underlie the emergence of a range of English courses in the whole of Indonesian. Indeed, irrespective of how the quality of the courses of English in Indonesia, the implied concern that a situation that is less good quality of teaching English in schools.
Logically, we can not be argued that courses in such English The growth in Indonesia if the results of teaching English at the school was satisfactory. If the case, then English is only intended for special interests to obtain a certificate as TOEFL, IELTS, and others and is not intended to improve the ability of English in daily life. But in reality, the majority of English courses that are intended to improve the ability of English in daily life, not for other goals.
Like in mathematics education, each student also recommended the English language have the ability to recognize the words in the English language of mathematics. UNY mathematics education in the existing international class which is the motivation for students to advanced in English-speaking, TOEFL and good conversation among students. Due to go to class in international mathematics education, students must meet the requirements - requirements that must be fulfilled. For example students should have already determined the TOEFL and have the average GPA - 3.5 or above average cum laude. In addition, the stages in the class with the national Indonesian language students are also taught about the use of words in the English language of mathematics. Because they are not denied this right now more and more schools - the schools and the most international in the entrance test to be employees of the use of English, although only slightly. Although learning the English language students will also have a lot of obstacles but it is all solved as follows. Some of the problems that, according to the students, preventing them to master English. The issues are:

1. Infrequently lecturers speak with English in the classroom. This is felt by preventing students because according to them, so they do not listen to other people speak English.
2. Subjects too on grammar (and not in the conversation), but students rarely are given directions on how and what the function of the elements of grammar that they learned it.
3. Vocabulary that is taught is not too useful in everyday conversation.

With problems such as the above, the mathematics education students must master the English language? English is the international language used by all countries in the world. The role and influence of the English language is very big in life, especially related to education, from the school with the lowest to the highest level of the Playgroup/ Kindergarten - Universities and in the world of work, the English language has also become a requirement if you want to get the absolute work in a company that both local and foreign. Therefore, can not be denied that the English language is important in although found in the control of a lot of obstacles, especially for countries that use English as a second language, one of which is Indonesian. which among others is still a lack of motivation and courage to speak English, still lack the knowledge of the English language, the mind set of people assume that English is difficult, After what the benefits and usefulness of English, What should be done in mathematics education students in the English language?
1. Learn every day
Try to allocate some time each day to learn English. Ideally the brain when we are able to receive well. Better to study 30 minutes per day than 3 hours per week. If it can provide time-per, try to share a 2 or 3 sessions. For those who work in office, may have only a few hours as in the rest. Most important is that we (students in mathematics education) can take the time to learn English even though the goods while.
2. Review regularly
Students repeat each material already learned several times. To give time to the brain for consider materials, but make sure that the distance of each material is not too long, for example, more than a few weeks. If not, students may concern forget what is learned. And ensure students have understood the content of the material before proceeding to the next.
3. Focus on things of interest
Once the students have to understand the basics of the English language, both flee practice reading / writing / speaking on matters of interest. In this way will be easier to remember words, phrases and grammatical. Because basically if we like something it will be easier to apply. For example through music. If you like to sing but not too interested in the English language, please start looking for songs that speak English well and we like singer well as voice and her or his face. If we pleased with the track, we will try to understand the meaning of music. Well, indirectly we have favor with the English language because that song.
4. Raise read books, articles, writing in the English language
At the beginning of the reading will have a lot of vocabulary that students do not know. Do not give up easily. interpret each word with the help of the dictionary, and write the meaning of the word underneath. If done continuously in a few weeks then we will stop to open the dictionary every 2 minutes to read any posts in kind.
5. Note sounding words
Indeed, sometimes very difficult to say a word the English language well, but not does not mean impossible. Slang will not be lost, but try to pay attention to pronunciation. The first must do is control of the alphabet, and then note that phonetik often included in the dictionary.
6. Raise vocabulary
Students spend approximately 15 minutes each day to learn new vocabulary. Can repeat with vocabulary obtained from the literature, tried consider song lyrics, or attempt to catch the film favored dialogue. Write a vocabulary that has been learned in a special book to write. With the vocabulary will not be lost.
7. Try write in English
No direct means must write articles or works of literature. Self-expression short sentences, followed by a short paragraph. Then try any posts in their own corrections. Do not always rely on Word Spelling Check, because this function can not be relied upon to check the grammar error.
Self-discipline and follow basic grammar rules with the patient. No need to hurry to write the sentence that is long and complex. Start with a short sentence with a simple vocabulary. For example in the task of the English language lecturers. Try re-write a story or conversation in the video that was shown when the lecturers teaching the English language course. Or try to write back to text speak Indonesian in the English language.

What I Have Done and What Will Do About English of Mathematics

English mathematics is one of the subjects in the whole semester. This course is a general course and consists of 2 SKS. in a week there one time and 100 minutes of each meeting. That I have got from studying the English language is writing, reading, listening and speaking - proficient.
At the beginning of the lecture, the lecturer ( Mr. Marsigit ) explain, describe and explain a basic topic or discussion about the English language using the English language. Temporary lecturers ( Mr. Marsigit ) teaching, my students and others who listen to all that is described, and are presented by lecturers.
In addition to listening to the lecturers and teaching, the lecturers also showed a video about the mathematics as an example: theorems about Pythagoras, exponent, power and root. Graphic intersects line, properties of logarithms, pre calculus, polynomial, Trigonometry, etc.
From anything that I have heard and I seen from the lecturers and from the video, and I noted the important principals. From the main principals that I have written before, and I developed become a paper that using the my own simple words, simple expressions and also a simple task.
From a summary of the essence and then I read again if there is confusion or lack of writing after in the task I have is correct, the task I collect form in and out of print in the blog posting each student. Before correct - correctly collected and the post we should know right from the paper's contents. If a teacher asked him about when paper’s contents that we made, we can explain and re-told the contents of the paper that the student that usually called talking. And that's all I ever have or do I have the task in accordance with the time specified by lecturer. I will do to study the English language is fill my blog with the paper that I collect and sum - sum subjects with complete English language.
Learn more learn by words - words in the English language and to read any posts to speak fluent English in order to pronounce any posts speak English and have a word - a word in the English language. With English I apply mathematics to fill blogs language in English I applied in reading blogs, magazines, novels, stories in the English language.

Summary of Video

Summary of Video

Video 1:

From that video, I think that we have to believe with our ability. We have to certain that we be able to doing something. If we have a dream, so we must sure that we can to reach our dream. Although the business need, but in the hearts denagn confidence that we can and can do. Nothing is impossible.

Video 2:

In second video, I am more know about mathematics. Mathematics learned geometry, trigonometry, ln x, significant figure, limit x approach boundlessly, exponent, integral e power x and from this video, I know that value of phi is 3,145…………

Video 3:

The third video show about mathematic problem solving.

If the function h(x)=g(2x)+2,what the value of h(1)?

Answer:

h(x)=g(2x)+2

h(1)=g(2x1)+2 g(2x1) = 1

h(1)=3

For example :

The graph of f(x) = x + 1 if 2f(p) = 20. How value of f(3p)?

Answer:

2f(p) = 20

f(p) = 10

f(x) = x + 1

we substitution p to f(x) = x + 1 become f(p) = p + 1

f(p) = p + 1 = 10

p = 10 – 1 = 9

f(3p)????

3p = 3(9) = 27

f(x) = x + 1

f(3p) = 3p + 1 = 27 + 1 = 28

So value of f(3p) is 28

Ø The xy- coordinat plane, the graph of x=y²- 4 intersects line ℓ at(0,p) and (5,t). what is the greates possible value slope?

Answer:

x = y²- 4

x	0	5
y	p	t

Video 4:

Video 4 about the properties of logarithm.

1. Log x to the base b equals y symmetry with b power y equal x

2. Log x to the base 10 equals Log x

3. Log x to the base natural numeral equals Ln x (this natural logarithm)

Example :

1.Log 100 to the base 10 equals x. How value of x?

2. Log x to the base 2 equals 3. How value of x?

3. Log 1 over 49 to the base 7 equals x. How value of x?

Answer :

1. Log 100 to the base 10 equals x, become 10 to the power of x equals 100, so x equal 2.

2. Log x to the base 2 equals 3, become 2 to the power of 3 equal x, so x equals 8.

3. Log 1 over 49 to the base 7 equals x, become 7 to the power of x equals 1 over 7 to the power of 2 in bracket. This similar with 7 to the power of x equals 7 to the power of minus 2, so x equal minus 2.

Ø Log M times N in bracket to the base b equals Log M to the base b plus Log N to the base b.

Ø Log M over N in bracket to the base b equals Log m to the base b minus Log N to the base b.

Ø Log x to the power of n in bracket to the base b equals n times Log x to the base b.

Example:

How value of Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in square bracket to the base 3?

Answer:

Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in bracket to the base 3

equals Log x to the power 2 times open bracket y plus 1 close bracket in square bracket to the base 3 minus Log z to the power 3 in bracket to the base 3

equals Log x to the power 2 to the base 3 plus Log open bracket y plus 1 close bracket to the base 3 minus Log z to the power 3 to the base 3

equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

So, Log x to the power of 2 times y plus 1 in bracket over open bracket z to the power of 3 close bracket in bracket to the base 3 equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

Video 5:

About Graph of Rational Function.

Example:

Draw a function of f(x) equals x plus 2 in bracket over x minus 1 in bracket

Answer:

f(x) = ( x + 2 ) / ( x – 1 )

even x = 1 we find f (x) = 3 / 0 ( this wrong and imposible ), so graph of f(x) not be able nudge line x = 1.

f(x) = 1 / (x +1)

And not all rational function denominator can be zero.

y = x² – x – 6 / x – 3

y = (x – 3) (x+2) / (x – 3)

y = (x+2) missing pointlopphole,

Video 6:

Video 6 consist about Trigonometry.

Sine (Sin), Cosine (Cos), and Tangents (Tan) are trigonometric ratios.

Ratio of Sin is opposite per hypotenuse (soh)

Ratio of Cos is adjoin per hypotenuse (cah)

Ratio of Tan is opposite per adjoin (toa)

The other trigomometric rations are represented as follows:

Secant (Sec) is one cos

Cosecant (Cos) is one sin

Cotangents (Cot) is one tan

For example:

If the right triangle ABC right angled at B where AB = 3 cm, BC = 4 cm, CA = 5 cm (hypotenuse). P is angle front of BC and Q is front of BA. How value of all trigonometric ratio?

Answer:

1. Sin P = opposite/hypotenuse = 4/5

Cos P = adjoin/hypotenuse = 3/ 5

Tan P = opposite/ adjoin = 4 /3

Cosec P = one sin = 5/ 4

Sec P = one cos =5/ 3

Cot P = one tan = 3/ 4

2. Sin Q = opposite/ hypotenuse =3/ 5

Cos Q = adjoin/ hypotenuse = 4/ 5

Tan Q = opposite/ adjoin = 3/ 4

Cosec Q = one sin = 5/ 3

Sec Q = one cos = 5 /4

Cot Q = one tan =4/ 3

Diffucult Word to Express Mathematical Idea

Diffucult Word to Express Mathematical Idea

Part I : (Diffucult word)

1. Hints

2. Chords

3. Arbitrary

4. Improper integrals

5. General continued fraction

6. Odd natural number

7. Complex modulus

8. Absolute square

9. Multi angle formulas

10. Number theory

11. Adding

12. Indeterminate linear equations

13. Quadratics equations

14. Second order

15. Equation with multiple variable

16. Exposition

17. Cramer rule

18. Conic sections

19. Axis

20. Intersection

21. Intersects

22. Point of intersection

23. Vertex

24. Edge

25. Matrix multiplication

26. Perimeter

27. Surface area

28. Circumference

29. Cut

30. The average value

31. Definite integral

32. Even function

33. Odd function

34. Tangent

35. Maximum value

36. Slices

37. Around the triangle

38. Right cylinder

39. Oblique cylinder

40. Bisecting line

41. Weight line

42. High line

43. Isosceles triangle

44. Equilateral triangle

45. Decline back

46. Diagonal

47. Rhombus

48. Permutation

49. Curve line

50. Collective settlement

51. Coordinates khutub

52. Bow belt

53. Arithmetic progression.

Part II: (The meaning of difficult word)

1. petunjuk

2. penghubung antara dua titik lingkaran

3. berubah – ubah

4. penanganan integral

5. pecahan umum

6. bilangan ganjil alami

7. harga mutlak komplek

8. kuadrat harga mutlak

9. rumus sudut banyak

10. teori bilangan

11. penambahan

12. persamaan kuadrat tak tentu

13. persamaan kuadrat

14. urutan ke dua

15. persamaan dengan variabel banyak

16. Penjelasan

17. aturan Cramer

18. bagian dari kerucut

19. poros

20. irisan

21. memotong

22. titik potong

23. titik puncak

24. rusuk

25. perkalian matriks

26. garis keliling

27. luas permukaaan

28. keliling

29. menyinggung

30. nilai rata-rata

31. integral tentu

32. fungsi genap

33. fungsi ganjil

34. garis singgung

35. nilai maksimum

36. irisan

37. keliling segitiga

38. silinder tegak

39. silinder condong / miring

40. garis bagi

41. garis berat

42. garis tinggi

43. segitiga sama kaki

44. segitiga sama sisi

45. tolak belakang

46. diagonal

47. belah ketupat

48. permutasi

49. garis lengkung

50. himpunan penyelesaian

51. koordinat khutub

52. tali busur

53. deret aritmatika

Part III : ( Application the difficult word in the sentence )

1. Center point of a curve into a center point of each strap through the bow's center.

2. O to be a central point of 2 polecat fruit called a tangent point knot.

3. On using symmetry of function called even function if fulfilling f(-x)=f(x).

4. A function called odd function if fulfilling f(-x)= -f(x).

5. For determining an average value of integration with fomula, definite integral from function f(x) divide by difference of the selang.

6. If two different angle decline back, so both of these are congruent.

7. An isosceles triangle is a triangle which both mutual sides are congruent.

8. An equilateral triangle is a triangle which third of the sides are congruent.

9. The circumference of triangle is the count of the third size of sides.

10. A segment called as weight line a side of triangle if the edges of the segment is point angle of triangle and mid point of sides in front of the point angle.

11. A diffraction line called as bisecting line of angle if the diffraction line is inside of the angle so the both angle which built is congruent.

12. A high line of triangle is a segment line which connecting a point into a triangle with a point on line that contain a side in front of the point angle.

13. A rhombus is parallelogram which a pair of the adjacent sides is congruent.

14. Every diagonal on a parallelogram divide into two same length .

15. If a side that bisector with a circle, cut the area inside of the circle, so the line cut right in two point on the circle.

16. If the components of cylinder perpendicular with the base, so the cylinder called as right cylinder.

17. Inverse of right cylinder is oblique cylinder.

18. Two cylinders called parallel, if the slices of the cylinder are on two parallel area.

19. Permutation is a formation which be built by entirety or a part of a group of thing.

20. Collective settlement can be the form of straight line.

21. Coordinate of khutub is used to determining situation of a point in a flat area.

22. Successive amount of tribes on arithmetic line called as arithmetic progression.

23. Arbitrary-precision mathematical calculations have to jump through many more hoops than just blindingly manipulating numbers.

24. An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration.

25. a line segment having endpoints which are points of a circle. EX. If the chord contains the center of the circle, it is called a diameter.

26. In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.

27. An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information.

28. Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.

29. By finding exact values of special trigonometric angles, verifying trigonometric identities, and solving trigonometric equations we show how to use the multiple angle formulas. We also show the connection between the multiple angle formulas and the addition and subtraction formulas and half angle formulas.

30. A second order differential equation is an equation involving the unknown function y, its derivatives y' and y'', and the variable x.

31. Cramer's rule is a theorem in linear algebra, which gives the solution of a system of linear equations or corresponding square matrices in terms of determinants.

32. a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a circular conical surface) with a plane. A conic section is therefore a restriction of a quadric surface to the plane.

33. A conic section is a section of a cone. The popular ellipse, parabola, and hyperbola, along with a few other mathematical shapes, can each be seen to be a section of a cone.

34. Any equation of type ax² + bx + c = 0 where a, b, and c are constants and , is in standard form for a quadratic equation.

35. Quadratic equations of type ax² + bx + c = 0 and ax² + bx = 0 (c is 0) can be factored to solve for x.

36. Drag any orange dot at the points A,B,P or Q. The line segments intersect at point K.

37. An intersection is a single point where two lines meet or cross each other.

38. Vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle , which is the 'top' corner opposite its base, but this is not its strict mathematical definition. Vertex typically means a corner or a point where lines meet.

39. number of edge equal to the number of cubes on the edge block.

40. we will cover a method for finding the point of intersection for two linear functions. That is, we will find the (x, y) coordinate pair for the point were two lines cross.

41. Matrix multiplication satisfies the rules (AB)C = A(BC) (associativity), and (A+B)C = AC+BC as well as C(A+B) = CA+CB (left and right distributivity), matrix multiplication is not commutative, in marked contrast to (rational, real, or complex) numbers whose product is independent of the order of the factors.

42. The perimeter of a polygon is the sum of the lengths of all its sides. What is the perimeter of a trapezoid having side-lengths 10 cm, 7 cm, 6 cm, and 7 cm? the perimeter is the sum 10 + 7 + 6 + 7 = 30cm.

43. The circumference is the distance around a closed curve. Circumference is a kind of perimeter. The circumference of the entire circle can be represented as twice the sum of the lengths of the infinitesimal arcs that make up this half circle. The length of a single infinitesimal part of the arc can be calculated using the Pythagorean formula for the length of the hypotenuse of a rectangular triangle with side lengths dx and f'(x)dx.

44. Even objects with smooth surfaces, such as spheres, have surface area. Also surface area is the area of the faces that cover a 3-D shape.

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