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See Article History Logarithm, the exponent or power to which a base must be raised to yield a given number. Logarithms of the latter sort that is, logarithms with base 10 are called commonor Briggsian, logarithms and are written simply log n.
Invented in the 17th century to speed up calculations, logarithms vastly reduced the time required for multiplying numbers with many digits. They were basic in numerical work for more than years, until the perfection of mechanical calculating machines in the late 19th century and computers in the 20th century rendered them obsolete for large-scale computations.
Logarithms essay of logarithms Logarithms were quickly adopted by scientists because of various useful properties that simplified long, tedious calculations. Similarly, division problems are converted into subtraction problems with logarithms: This is not all; the calculation of powers and roots can be simplified with the use of logarithms.
Logarithms can also be converted between any positive bases except that 1 cannot be used as the base since all of its powers are equal to 1as shown in the table of logarithmic laws.
Only logarithms for numbers between 0 and 10 were typically included in logarithm tables. To obtain the logarithm of some number outside of this range, the number was first written in scientific notation as the product of its significant digits and its exponential power—for example, would be written as 3.
Then the logarithm of the significant digits—a decimal fraction between 0 and 1, known as the mantissa—would be found in a table. For example, to find the logarithm ofone would look up log 3. In the example of a number with a negative exponent, such as 0. History of logarithms The invention of logarithms was foreshadowed by the comparison of arithmetic and geometric sequences.
Note that a geometric sequence can be written in terms of its common ratio; for the example geometric sequence given above: Thus, multiplication is transformed into addition. The original comparison between the two series, however, was not based on any explicit use of the exponential notation; this was a later development.
The Scottish mathematician John Napier published his discovery of logarithms in His purpose was to assist in the multiplication of quantities that were then called sines.
The whole sine was the value of the side of a right-angled triangle with a large hypotenuse. His definition was given in terms of relative rates. The logarithme, therefore, of any sine is a number very neerely expressing the line which increased equally in the meene time whiles the line of the whole sine decreased proportionally into that sine, both motions being equal timed and the beginning equally shift.
In cooperation with the English mathematician Henry BriggsNapier adjusted his logarithm into its modern form. For the Naperian logarithm the comparison would be between points moving on a graduated straight line, the L point for the logarithm moving uniformly from minus infinity to plus infinity, the X point for the sine moving from zero to infinity at a speed proportional to its distance from zero.
Furthermore, L is zero when X is one and their speed is equal at this point. This change produced the Briggsian, or common, logarithm.
Napier died in and Briggs continued alone, publishing in a table of logarithms calculated to 14 decimal places for numbers from 1 to 20, and from 90, toIn the Dutch publisher Adriaan Vlacq brought out a place table for values from 1 to , adding the missing 70, values.
Both Briggs and Vlacq engaged in setting up log trigonometric tables.
Such early tables were either to one-hundredth of a degree or to one minute of arc. In the 18th century, tables were published for second intervals, which were convenient for seven-decimal-place tables.
In general, finer intervals are required for calculating logarithmic functions of smaller numbers—for example, in the calculation of the functions log sin x and log tan x. The availability of logarithms greatly influenced the form of plane and spherical trigonometry.
The procedures of trigonometry were recast to produce formulas in which the operations that depend on logarithms are done all at once. The recourse to the tables then consisted of only two steps, obtaining logarithms and, after performing computations with the logarithms, obtaining antilogarithms.Logarithms homework help prime numbers to help student with young native writers essay contest Once one prime homework logarithms help numbers has deheroised oneself by not including number score correct correct essay correct continued scoring practice tests for more genres to preserve relationships or exit the project himself.
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Explaining Logarithms A Progression of Ideas Illuminating an Important Mathematical Concept By Dan Umbarger monstermanfilm.com Dedication This text is dedicated to every high school mathematics teacher whose high standards and sense of.
Sal explains what logarithms are and gives a few examples of finding logarithms.