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单词 Logarithmic functions
释义

Logarithmic functions

中文百科

对数 Logarithm

(重定向自Logarithmic functions)
20世纪的常用对数表的一个实例。

在数学中,数 x(对于底数 β)的对数是 β 的指数 y,使得 x=β。底数 β 的值一定不能是1或0(在扩展到复数的复对数情况下不能是1的方根),典型的是e、 10或2。数x(对于底数β)的对数通常写为

y=\log_\beta x\!

称作为以β为底x的对数。 当xβ进一步限制为正实数的时候,对数是1个唯一的实数。 例如,因为

3^4 = 3 \times 3 \times 3 \times 3=81

我们可以得出

4=\log_3 81\!

用日常语言说,以3为底81的对数是4。

英语百科

Logarithm 对数

(重定向自Logarithmic functions)
The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log2(8) = 3, because 23 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it.
Logarithm in base 2-10 of numbers 1-10. Line labels = number. X axis = base. Y axis = logarithm.
The 1797 Encyclopædia Britannica explanation of logarithms
Schematic depiction of a slide rule. Starting from 2 on the lower scale, add the distance to 3 on the upper scale to reach the product 6. The slide rule works because it is marked such that the distance from 1 to x is proportional to the logarithm of x.

In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication. For example, the base 10 logarithm of 1000 is 3, as 10 to the power 3 is 1000 (1000 = 10 × 10 × 10 = 10); the multiplication is repeated three times. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1. The logarithm of x to base b, denoted logb(x), is the unique real number y such that

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