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natural logarithm(옄뿰濡쒓렇)-쐞궎뵾뵒븘 옄猷 씤슜
 源以슚    | 2007쨌07쨌07 22:32 | HIT : 13,848 |
[븘옒 궡슜 씠쇅뿉 蹂대떎 옄꽭븳 궡슜 natural logarithm- google.com 뿉꽌 寃깋빐 蹂댁떆湲 諛붾엻땲떎.]

Natural logarithm
From Wikipedia, the free encyclopedia

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

In simple terms, the natural logarithm of a number x is the power to which e would have to be raised to equal x - for example the natural log of e itself is 1 because e1[二: e쓽 1듅] = e, while the natural logarithm of 1 would be 0, since e0[二: e쓽 0듅] = 1 (see the x-intercept of the graph).
The natural logarithm can be defined for all positive real numbers x as the area under the curve y = 1/t from 1 to x, and can also be defined for non-zero complex numbers as explained below.

[洹몃옒봽 깮왂]
Graph of the natural logarithm function.
The function goes to negative infinity as x approaches 0, but grows slowly to positive infinity as x increases in value.The natural logarithm function can also be defined as the inverse function of the exponential function, leading to the identities:

In other words, the logarithm function is a bijection from the set of positive real numbers to the set of all real numbers. More precisely it is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition.

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

Contents [hide]
1 Notational conventions
2 Reason for being "natural"
3 Definitions
4 Derivative, Taylor series
5 The natural logarithm in integration
6 Numerical value
6.1 High precision
6.2 Computational complexity
7 Complex logarithms
8 See also
9 External links
10 References

[edit] Notational conventions

Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean loge(x), i.e., the natural logarithm of x, and write "log10(x)" if the base-10 logarithm of x is intended.
Some engineers, biologists, and some others generally write "ln(x)" (or occasionally "loge(x)") when they mean the natural logarithm of x, and take "log(x)" to mean log10(x) or, in the case of some computer scientists, log2(x).
In most commonly-used programming languages, including C, C++, Fortran, and BASIC, "log" or "LOG" refers to the natural logarithm.
In hand-held calculators, the natural logarithm is denoted ln, whereas log is the base-10 logarithm.

[edit] Reason for being "natural" [옄뿰濡쒓렇씪 移븯뒗 씠쑀-븘옒뿉 씪遺 踰덉뿭臾]

Initially, it seems that in a world using base 10 for nearly all calculations, this base would be more "natural" than base e. The reason we call the ln(x) "natural" is two-fold: first, expressions in which the unknown variable appears as the exponent of e occur much more often than exponents of 10, and second, because the natural logarithm can be defined quite easily using a simple integral or Taylor series - this is not true of other logarithms. Thus, the natural logarithm is more useful in practice. To put it concretely, consider the problem of differentiating a logarithmic function:

If the base b is equal to e then the derivative is simply 1/x, and at x = 1 the slope of the graph is 1.

There are other reasons the natural logarithm is natural; there are a number of simple series involving the natural logarithm, and it often arises in nature. In fact, Nicholas Mercator first described them as log naturalis before calculus was even conceived.

슦由ш 옄뿰濡쒓렇씪 移븯뒗 씠쑀뒗 몢 媛吏씠떎.
癒쇱, 誘몄쓽 蹂닔뱾씠 10쓽 吏닔蹂대떎뒗 e쓽 吏닔媛 썾뵮 옄二 굹궃떎.
洹몃━怨, 떒닚븳 쟻遺꾩씠굹 뀒씪윭 떆由ъ쫰瑜 씠슜븯뿬 옄뿰濡쒓렇媛 留ㅼ슦 돺寃 젙쓽릺湲 븣臾몄씠떎.
洹몃윭誘濡, 옄뿰濡쒓렇뒗 떎젣뿉꽌 蹂대떎 쑀슜븯떎.
援ъ껜쟻쑝濡쒕뒗, 濡쒓렇븿닔瑜 誘몃텇븯뒗 臾몄젣瑜 깮媛곹빐 蹂닿린 諛붾떎.
옄뿰濡쒓렇씪 移븯뒗 삉 떎瑜 씠쑀뱾씠 엳떎. 옄뿰濡쒓렇瑜 룷븿븯뒗 떒닚븳 湲됱닔媛 留롮씠 엳쑝硫, 옄뿰뿉꽌 醫낆쥌 굹궃떎. 떎濡, 땲肄쒕씪뒪 癒몄씠꽣뒗 理쒖큹濡 洹몃뱾쓣 [濡쒓렇 굹닾엫由ъ뒪]씪 移븯뒗뜲, 씠뒗 誘몄쟻遺꾪븰씠 븘吏 젙由쎈릺湲 쟾씠뿀떎.

[썑왂]

* 옄뿰濡쒓렇쓽 諛묒닔 e瑜 븿猿 뿰援ы븿씠 醫뗪쿋뒿땲떎.
  
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