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Logarithm Online VideoTI Calculator Tutorial: Logarithms
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 Briggs , Napier 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, to , In 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.
Info Print Print. Table Of Contents. Submit Feedback. Thank you for your feedback. Introduction Properties of logarithms History of logarithms. Home Science Mathematics.
Francis J. Author of Mathematical Machines. See Article History. Properties of logarithms Logarithms were quickly adopted by scientists because of various useful properties that simplified long, tedious calculations.
Britannica Premium: Serving the evolving needs of knowledge seekers. Subscribe Now. Learn More in these related Britannica articles:. This is because 10, is equivalent to 10 to the power of 4.
Thus, just as division is the opposite mathematical operation to multiplication, the logarithm is the opposite operation to exponentiation.
Traditionally, a base of 10 is assumed in logarithms, but a base can be any number except 1. The binary logarithm of x is typically written as log 2 x or lb x.
However, a base of e is typically written as ln x and rarely as log e x. As illustrated above, logarithms can have a variety of bases. A binary logarithm, or a logarithm to base 2, is applied in computing, while the field of economics utilizes base e , and in education base 10, written simply as log x, log 10 x or lg x, is used.
By organizing numbers according to these bases, real numbers can be expressed far more simply. Custom Base Logarithm: log.
Natural Logarithm Base e : ln. Base Logarithm: lg.