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单词 logarithm
释义

logarithm

Let a, x be positive numbers with a ≠ 1. Then logax, the logarithm of x to base a, is defined by

where ln denotes the logarithmic function. This is equivalent to saying that y = logax if and only if x = ay or that the function logax is the inverse function of ax. The following properties hold, where x, y, and r are real, with x,y > 0:

(i) loga(xy) = loga x + loga y.
(ii) loga(1/x) = −loga x.
(iii) loga(xr) = r loga x.
(iv) Logarithms to different bases are related by the formula

(v) inline

Logarithms to base 10 are called common logarithms. Logarithms to base e are called natural logarithms. See complex logarithm.

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更新时间:2025/4/29 9:56:11