A Complex "MATH" Calculation Tool

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Posted in Wikinut>Guides>Science>Numbers And Maths

Mathematics is a subject that should be taught both in elementary, junior high, or high school. In high school Math material usually taught is the development of materials in education before, such as logarithms. Logarithm is a Mathematical operation that is the inverse of the exponent or the rank.

What does it mean?

Logarithm is often used to solve the equations that rank is unknown. In the world of mathematics, we recognize various symbols operations, including the most familiar such "+" as a symbol of the command to "Sum" or × as a symbol of the command to "Multiply". And the symbol of command whether the logs? In general, the base of logarithm is follows:

a log b = c ó ac = b
With: a > 0, a ≠ 1, b> 0

  • It is called the cardinal number of logarithm or base
  • It is called the numbers on the logarithmic
  • It is called the base of logarithm results or the 10 cardinal number should not be written.

And or the most of logarithm basic formula below:

    a^c = b → ª log b = c
    a = base
    b = logarithm numbers
    c = results logarithm

For example:
2 log 8 = 3 ó 23 = 8,5 log
125 = 3 ó 53 = 125


The properties of Logarithms:

  • ª log a = 1
  • ª log 1 = 0
  • ª log aⁿ = n
  • ª log bⁿ = n • ª log b
  • ª log b • c = ª log b + ª log c
  • ª log b/c = ª log b – ª log c
  • ªˆⁿ log b m = m/n • ª log b
  • ª log b = 1 ÷ b log a
  • ª log b • b log c • c log d = ª log d
  • ª log b = c log b ÷ c log a

The Operation log is one of the triumvirates of root operations, and log rank. If each operation reworded into a language of symbols, then all the three will form a relationship between the commands as follows:

    Operating rank: ab = x
    Root operation: = a
    Operation log:

If known the rank operation is "ab = x", in the root operation, which was ordered is to find “a” rank of the operation, and in the operation log, which commanded the operation is to find “b” rank of the root operation. Then for “a” is in the operation quantity raised to the rank is, while b is the quantity rank.
So, in a statement 10Log 100, what we are commanded to seek the rank of number 10 which makes 10 that it could be change to the value of 100. Because the 10 squared is 100, and then the answer to that statement is 2, which a number that makes the 10 changing to the 100 value.

The Complex Calculations

Before the advent of calculators, logarithms become an important tool to help perform very complex calculations. This is because the ability of the logarithm to change the operation of multiplication of the numbers are very big into operation the sum of the numbers are much smaller but with the same results accurate. As an illustration of the simplicity of calculations using logarithms, suppose there is a multiplication of the following:

    100,000 × 1,000,000

The multiplication above is involving the two of large numbers, and that is the numbers with 6 digits and 7 digits and these numbers generated is 12 digits. By logarithm, calculation of two very large numbers that can be converted into the sum of two numbers with each no more than one digit only, namely:

    10log 100.000 + 10log 1.000.000
    =>> 5 + 6 = 11

    And it is just produced no more than 2 digits only!

By using antilogarithms table, we can determine what is the equivalent of 11 is, and that is the produce of the two large numbers of us. We no longer need to bother to perform the calculations of multiplication are very long and tiring. All we need is just a tool in the form of a table of logarithms and anti-logarithms, and then perform a very simple summation operation.

The Rationale & The Real Simple of Logarithm

The rationale behind in the real simple of Logarithm, which is make the 2 rows of numbers. Which is a geometric sequence with initial rate is 1. The ratio between the numbers of free, but we suppose the ratio between the closest numbers is 2 times. Thus, the number of the second term is 2 times the number of the first rate; the third-rate number is 2 more then times of the number of the second term, and so on. So, we have a geometric sequence are:

    1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Then create another sequence of numbers, but this time arithmetic sequence. Numbers first rate is 0. The difference between the closest numbers is up, but for the sake of simplicity, we make only difference is 1. So, the arithmetic sequences that we have are:

    0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

We put the line geometry and arithmetic sequences are adjacent to each other to be as follows:

  • 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192
  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

What is interesting from the two rows of numbers above are as follows:

  1. If we add up the two members of the second row of numbers, then the result of numbers would be in to the same position with the number of multiplication results from the two members of the first sequence of numbers, that are both parallel to the two fruit member first sequence number.
  2. For example, if we add the 4 and 5 will we get the number 9. In the above number 4, there are 16 numbers, and the above numbers 5, there are 32 numbers. If we make a multiply to the numbers 16 and 32, the we find an answer is 512. So then, where numbers 512 is? Absolutely it is just above to the number 9!.
  3. What distinguishes between the logarithm that we learned in school and our calculation from the example above? Of course, that is the logarithm we learn, and the two rows of numbers used are:
    • 1, …., 10, …, 100, …, 1000, …, 10000
    • 0, …., 1, …, 2, …, 3, …, 4

So, the points is between in the two of numbers in the second row above are the whole numbers that are in between the two numbers with the ratio and difference respectively.
Just take a look a video below. Definitely this Video finally Makes Sense of Logarithms

By the way, this video uses the medium of Sharpie and notepad to finally help you make sense of logarithms, once and for all. Turns out, they are not as complicated as you may have thought. Thank you very much Vi Hart who made the videos.

The Inventors of Logarithm

There must be wondering that who is the inventor of this logarithmic theory? And a person who was a figure behind the genius idea to transform a complex multiplication process into a simple summation process? Was a Scottish Mathematician named John Napier (1150-1617). But, the idea developed by Napier logarithmic with base number was not 10 as we know it today. Napier prefer numbers are closely related to the size of the earth, and it is number the ten rank seven (10^7) = 10,000,000. The numbers then become part of the base number chosen by Napier.
For 20 years, Napier performs careful calculation to establish a table of logarithms. The struggle for 20 years it generates a table of logarithms with a range of values between 5 and 10 million. Logarithm term used by Napier and this "word" was the result of a combination of the two words, namely the "LOGOS" which means the "Ratio", and "ARITHMOS" which means "Numbers". In 1614, Napier's work was published under the title: “Mirifici Logarithmorum Canonis Descriptio” (Description Beautiful Rules of logarithm).
After the work was published in 1614, the other from the British mathematician named Henry Briggs (1561-1630), who was amazed by the work of Napier, Napier came. During the meeting, Briggs proposes to use the base of number 10 because it is simpler. Napier approves the proposal. There exist a number 10 as a new base of logarithms. Logarithm to the base 10 number is then we learn in mathematics at school until now.

Conclusion and Data Credits

Logarithms were first propounded in 1614, in a book entitled "Mirifici Logarithmorum Canonis Descriptio," by John Napier. (Joost Bürgi in Switzerland independently discovered logarithms, but did not publish his discovery until four years after Napier). Before the invention of calculators and computers, they made difficult calculations more feasible, helping to advance astronomy, surveying, navigation and mathematics. Napier also used some of his mathematical talents in theology and believed that his book predicting the Apocalypse was his most important work. He was convinced the end of the world would be in 1688 or 1700 - but died in 1617, so was not around to find that he was wrong on that one!.
Sure, that is the basic formula of logarithms. It looks a bit complicated for new learning. But it can be overcome with a lot of learning and practice. And for more information go and find it here! or you would like to know more about these Mathematicians expert. Just go and checking them below:

  1. Sir John Napier:
  2. Henry Briggs;

Note:
The syntax of logarithm internationally and in my home country is slightly different in terms of laying for the base (basis) number.

  • In a manner of writing Indonesia, the basis logarithm - "a" of "b" is written as ª log b.
  • While the procedures for International writing, the logarithm base "a" of "b" is written as log_a b.

Finally, in this paper I describe it using my national language versions, and it aims to avoid mistakes in the discussion. Besides that, I realize that there are many errors in the equivalent words and sentences in accordance with the standard of English language. Surely, just make you understand. I wish to all of you many thanks for stopping by to read this page.

"LOGARITHM" - ©2015| viewgreen for the Wikinut - Unique Contents.

References*:

Images take from^: Wikipedia^ & Nationalgalleries^
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Tags

Antilogarithms, British, Calculations, Complex, Digit, Exponential, Formula, Inverse, Logarithm, Mathematics, Multiplication, Numbers, Operation, Rank, Research, Root, School, Sum, Symbols, Table

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author avatar viewgreen
A CS engineer who loves to write about TI (Innovations), Socials, Cultures & Heritage (Local Wisdom), Humors and others that I am eager and interested to. Thank you! :D

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Comments

author avatar viewgreen
1st Feb 2015 (#)

Thank you sir for the approval to publish this page. Have a nice day to you. cc: ~ (Steve Kinsman)

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author avatar Carol Roach
1st Feb 2015 (#)

I was always bad at math, I can't trust myself to even count money

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author avatar viewgreen
2nd Feb 2015 (#)

Haha... you are right madam, not too many people like Math. But I'm not sure if they couldn't count the money in their own pocket. Lol! :) Thank you for stopping by madam.

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author avatar puncakceria
2nd Feb 2015 (#)

interesting article..

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author avatar viewgreen
2nd Feb 2015 (#)

Thank you my friend puncakceria! where you have been so long by the way?. Appreciate for you coming back.

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author avatar Ptrikha
2nd Feb 2015 (#)

Great article on mathematics.

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author avatar viewgreen
3rd Feb 2015 (#)

Thank you my friend Ptrikha! for stopping by!

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author avatar Utah Jay
2nd Feb 2015 (#)

I have a real hard time with math after my stroke.

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author avatar viewgreen
3rd Feb 2015 (#)

Well, sir! I wish the thing that you've experienced is Math only, and of course the others things may not be and remain to write. Thank you for stopping by to read this page sir. :)

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author avatar M G Singh
3rd Feb 2015 (#)

Great post

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author avatar viewgreen
3rd Feb 2015 (#)

Thank you for stopping by sir!

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author avatar Shamarie
4th Feb 2015 (#)

Great article on Logarithm and congrats on the star page! Math was never my favorite subject, but it is always great to learn a new technique on the subject. Thanks for sharing!

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author avatar viewgreen
4th Feb 2015 (#)

Thank you my friend Shamarie! Yeah! that's true and some of my friends are the same too. At least this we know it even not too many. Thank you for stopping here my friend.

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author avatar Gclick
12th Feb 2015 (#)

Am hate Math, but this is a great job my friend. Congrat! on the star page. thanks.

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author avatar Colekdikit
13th Feb 2015 (#)

It's very educative posting and good job my friend. thanks

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