- Contents
- A Complete Table Of Common Logarithm And Antilogarithm For Mathematics Students
- History of logarithms
- A Table of The Common Logarithm
- History of logarithms

Logarithms. A Progression of. Ideas Illuminating an. Important Mathematical Concept. By Dan Umbarger starucarulrap.ga Brown Books Publishing . Logarithms appear in all sorts of calculations in engineering and science, If we had a look-up table containing powers of 2, it would be straightforward to look. Mathematics Learning Centre. Introduction to. Exponents and Logarithms. Christopher Thomas [email protected] University of Sydney.

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LOGARITHM l. Basic Mathematics. 1. 2. Historical Development of Number System. 3. 3. Logarithm. 5. 4. Principal Properties of Logarithm. 7. 5. Basic Changing. (b) Logarithm Laws are used in Psychology, Music and other fields of This involved using a mathematical table book containing logarithms. elementary functions (trigonometric, logarithmic, exponential, hyperbolic, etc.) as well as data from their books for use in several tables of this handbook.

Tables of logarithms[ edit ] A page from Henry Briggs ' Logarithmorum Chilias Prima showing the base common logarithm of the integers 0 to 67 to fourteen decimal places. Part of a 20th-century table of common logarithms in the reference book Abramowitz and Stegun. A page from a table of logarithms of trigonometric functions from the American Practical Navigator. Columns of differences are included to aid interpolation. Mathematical tables containing common logarithms base were extensively used in computations prior to the advent of computers and calculators , not only because logarithms convert problems of multiplication and division into much easier addition and subtraction problems, but for an additional property that is unique to base and proves useful: Any positive number can be expressed as the product of a number from the interval [1,10 and an integer power of This can be envisioned as shifting the decimal separator of the given number to the left yielding a positive, and to the right yielding a negative exponent of Only the logarithms of these normalized numbers approximated by a certain number of digits , which are called mantissas , need to be tabulated in lists to a similar precision a similar number of digits. These mantissas are all positive and enclosed in the interval [0,1. The common logarithm of any given positive number is then obtained by adding its mantissa to the common logarithm of the second factor. This logarithm is called the characteristic of the given number. Since the common logarithm of a power of 10 is exactly the exponent, the characteristic is an integer number, which makes the common logarithm exceptionally useful in dealing with decimal numbers. For numbers less than 1, the characteristic makes the resulting logarithm negative, as required. Early tables[ edit ] Michael Stifel published Arithmetica integra in Nuremberg in which contains a table [27] of integers and powers of 2 that has been considered an early version of a logarithmic table. The English mathematician Henry Briggs visited Napier in , and proposed a re-scaling of Napier's logarithms to form what is now known as the common or base logarithms. Napier delegated to Briggs the computation of a revised table, and they later published, in , Logarithmorum Chilias Prima "The First Thousand Logarithms" , which gave a brief account of logarithms and a table for the first integers calculated to the 14th decimal place.

For example, if you want to find the log of Slide your finger along that row to the right to find column 2. You will be pointing at the number Write this down. If your log table has a mean difference table, slide your finger over to the column in that table marked with the next digit of the number you're looking up. For Your finger is currently on row 15 and column 2. Slide it over to row 15 and mean differences column 7. Add the numbers found in the two preceding steps together.

This is the mantissa of the logarithm of Add the characteristic. Since 15 is between 10 and 10 1 and 10 2 , the log of 15 must be between 1 and 2, so 1.

Combine the characteristic with the mantissa to get your final answer. Find that the log of Method 3. Understand the anti-log table. Use this when you have the log of a number but not the number itself.

If you have x, find n using the log table. If you have n, find x using the anti-log table. The anti-log is also commonly known as the inverse log. Write down the characteristic. This is the number before the decimal point. If you're looking up the anti-log of 2.

Mentally remove it from the number you're looking up, but make sure to write it down so you don't forget it - it will be important later. Find the row that matches the first part of the mantissa. Most anti-log tables, like most log tables, have two digits in the leftmost column, so run your finger down that column until you find.

Slide your finger over to the column marked with the next digit of the mantissa. For 2. This should read If your anti-log table has a table of mean differences, slide your finger over to the column in that table marked with the next digit of the mantissa. Make sure to keep your finger in the same row. In this case, you will slide your finger over to the last column in the table, column 9. The intersection of row.

Write that down. Add the two numbers from the two previous steps.

In our example, these are and Add them together to get Use the characteristic to place the decimal point. Our characteristic was 2. This means that the answer is between 10 2 and 10 3 , or between and In order for the number to fall between and , the decimal point must go after three digits, so that the number is about rather than 70, which is too small, or , which is too big.

So the final answer is Method 4. Understand how to multiply numbers using their logarithms. So, the sum of the logarithms of two different numbers is the logarithm of the product of those numbers. We can multiply two numbers of the same base by adding their powers. Look up the logarithms of the two numbers you want to multiply.

Use the method above to find the logarithms.

For example, if you want to multiply Add the two logarithms to find the logarithm of the solution. In this example, add 1. This number is the logarithm of your answer. Look up the anti-logarithm of the result from the above step to find the solution.

You can do this by finding the number in the body of the table closest to the mantissa of this number The more efficient and reliable method, however, is to find the answer in the table of anti-logarithms, as described in the method above.

For this example, you will get Yes No. Not Helpful 7 Helpful Multiply 3. Now, divide this by 10 to get your log with base Not Helpful 10 Helpful You now have enough significant digits to follow method 2 in the article.

Not Helpful 22 Helpful Say you want to find the log of 9. Now that you have the correct number of significant digits, you can use a log table as long as you deal with decimal points correctly. Not Helpful 35 Helpful As long as the quotient is an exponent, you can use the normal method to find the antilog.

Not Helpful 23 Helpful Then add 3 as is between and Answer is 3.

Not Helpful 12 Helpful Choose the base you want to use. Write the numbers down the left side and the numbers across the top. Use a calculator or spreadsheet to calculate the log for each space in the table. Not Helpful 28 Helpful You can express this as 46 x 10 to the power The next step is to find log 46 , then multiply it with 10 to the power This allowed the user to directly perform calculations involving roots and exponents.

This was especially useful for fractional powers. In , Nathaniel Bowditch , described in the American Practical Navigator a "sliding rule" that contained scales trigonometric functions on the fixed part and a line of log-sines and log-tans on the slider used to solve navigation problems.

In , Paul Cameron of Glasgow introduced a Nautical Slide-Rule capable of answering navigation questions, including right ascension and declination of the sun and principal stars.

There Edwin Thacher's cylindrical rule took hold after From Wikipedia, the free encyclopedia. Main article: Common logarithm. Natural logarithm. Napierian logarithm. Slide rule. The Development of Logarithms by Henry Briggs". The Mathematical Gazette.

Retrieved Johannes and Jakob Meursius, On page , Proposition CIX, he proves that if the abscissas of points are in geometric proportion, then the areas between a hyperbola and the abscissas are in arithmetic proportion.

This finding allowed Saint-Vincent's former student, Alphonse Antonio de Sarasa, to prove that the area between a hyperbola and the abscissa of a point is proportional to the abscissa's logarithm, thus uniting the algebra of logarithms with the geometry of hyperbolas.

Alphonse Antonio de Sarasa, Solutio problematis a R. Marino Mersenne Minimo propositi Sarasa's critical finding occurs on page 16 near the bottom of the page , where he states: Enrique A. Springer, , page Sarasa realized that given a hyperbola and a pair of points along the abscissa which were related by a geometric progression, then if the abscissas of the points were multiplied together, the abscissa of their product had an area under the hyperbola which equaled the sum of the points' areas under the hyperbola.

That is, the logarithm of an abscissa was proportional to the area, under a hyperbola, corresponding to that abscissa. This finding united the algebra of logarithms with the geometry of hyperbolic curves. Springer, , pp. O'Connor; E. Mathematics in Ancient Iraq: A Social History. Select essays , Popular Prakashan, p. Shelley , Precalculus mathematics , New York: Holt, Rinehart and Winston, p.

University [of Prague] Press, Available on-line at: Neither the table nor the instructions were published, apparently only proof sheets of the table were printed. The contents of the instructions were reproduced in: Johannisschule, , pages 26 ff. William Blackwood , p. Mathematical Association of America. Peale reprint , 17 9th ed. A Manual. Archived from the original on 14 February It is a Math Solver.

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