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单词 Hyperbolic logarithm
释义

Hyperbolic logarithm

中文百科

自然对数 Natural logarithm

（重定向自Hyperbolic logarithm）
自然对数 ln(x) 的函数图像。
双曲线扇形是笛卡尔平面(x,y)上的一个区域，由从原点到(a, 1/a)和(b, 1/b)的射线，以及双曲线 xy = 1围成。在标准位置的双曲线扇形有a = 1且b > 1，它的面积为ln(b)[2]，此时双曲线扇形对应正双曲角。
当直角双曲线下的两段面积相等时，x的值呈等比数列，x2/x1=x1/x0=k，y的值也呈等比数列，y2/y1=y1/y0=1/k。
ln(a)展现为曲线 f(x) = 1/x从1至a下的面积。如果a小于1，从a到1的面积计为负数。

自然对数（Natural logarithm）是以e为底数的对数函数，标记作ln(x)或loge(x)，其逆函数是指数函数e。

英语百科

Natural logarithm 自然对数

（重定向自Hyperbolic logarithm）
Graph of the natural logarithm function. The function slowly grows to positive infinity as x increases and slowly goes to negative infinity as x approaches 0 (
The hyperbola y = 1/x (red curve) and the area from x = 1 to 6 (shaded in orange). This area equals the natural logarithm of 6.
ln(a) illustrated as the area under the curve f(x) = 1/x from 1 to a. If a is less than 1, the area from a to 1 is counted as negative.

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x) or log(x). This is done in particular when the argument to the logarithm is not a single symbol, to prevent ambiguity.
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更新时间：2025/6/20 20:07:05