The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2.718281828459...

In other words, the logarithmfunction is a bijection from the set of positive real numbers to the set of all real numbers.

Logarithms can be defined to any positive base other than 1, not just e, and they are always useful for solving equations in which the unknown appears as the exponent of some other quantity.

Logarithms were originally invented for the sake of abbreviating arithmeticalcalculations, as by their means the operations of multiplication and division may be replaced by those of addition and subtraction, and the operations of raising to powers and extraction of roots by those of multiplication and division.

The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284...

The logarithms are strictly Napierian, and the arrangement is identical with that in the canon of 1614.

Logarithms convert multiplication to addition, division to subtraction (making them isomorphisms between the field operations), exponentiation to multiplication, and roots to division (making logarithms crucial to slide rule construction).

Logarithms are useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.

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Logarithms determine n when given x; n is the number of times that x must be divided by b to reach 1.

One simply found the logarithms of both numbers (multiply and divide) or the first number (power or root, where one number is already an exponent) in a table of common logarithms, performed a simpler operation on those, and found the result on a table.

In abstract algebra, this property of the logarithmfunctions can be summarized by noting that any logarithmfunction with a fixed base is a groupisomorphism from the group of strictly positive real numbers under multiplication to the group of all real numbers under addition.

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Binarylogarithms are useful in determining characteristics of functions, such as the order of such functions that exhibit this behaviour.

Logarithms are also useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.

The logarithm, 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.

The logarithm of the number 70 is 1.84510, and the logarithm of the number 700 is 2.84510.

Logarithms had reached their full potential and most of what was done after 1694 was calculatinglogarithms to different bases.

One important difference between the logarithmfunction and most other mathematicalfunctions is that there are different varieties or flavors of the logarithmfunction.

First, the scale of the logarithmic axis represents the log of a variable; however, the axis is labeled using the values of the original variable.

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logarithmLOGARITHM[logarithm] [Grrelation number], number associated with a positivenumber, being the power to which a third number, called the base, must be raised in order to obtain the given positivenumber.

For example, the logarithm of 100 to the base 10 is 2, written log 10 100=2, since 10 2 =100.

He invented logarithms and wrote Mirifici logarithmorum canonis descriptio (1614), containing the first logarithmictable and the first use of the word logarithm.

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Logarithm is the exponent to which a number is raised to produce a given number.

The common logarithm, commonly abbreviated as log, refers to the exponent to which 10 has to be raised, and the natural logarithm, abbreviated ln, refers to the exponent to which e has to be raised.

A logarithm is an exponent used in mathematicalcalculations to depict the perceived levels of variable quantities such as visible light energy, electromagnetic field strength, and sound intensity.

When the base-10logarithm of a quantity increases by 1, the quantity itself increases by a factor of 10.

The logarithm is perhaps the single, most useful arithmetic concept in all the sciences; and an understanding of them is essential to an understanding of many scientific ideas.

Logarithms may be defined and introduced in several different ways.

Radioactivity behaves in such a way that the number N of radioactive atoms remaining at a later time t is given by a linear variation of the logarithm of N with t.

The sum of lines stabilizes the natural logarithm, as was to be shown.

The integral on a surface, excepting an obvious case, essentially counterbalances the decreasing natural logarithm that will undoubtedly lead us to to true hard cock The criterion stabilizes a maximum, obviously showing all bosh of the aforesaid.

It is necessary to note, that integral develops the natural logarithm, thus, instead of 13 it is possible to take any other constant.