V2EX antilogarithm

Antilogarithm

Definition / 释义

反对数;反对数值:与“对数(logarithm)”相反的运算结果。若 \(\log_b(x)=y\),则 \(x\) 是 \(y\) 的以 \(b\) 为底的反对数,记作 \(\text{antilog}_b(y)=b^y\)。(在自然底数 \(e\) 下常对应指数函数 \(e^y\)。)

Pronunciation / 发音

/n.til..r.m/

Examples / 例句

The antilogarithm of 2 in base 10 is 100.
以 10 为底时,2 的反对数是 100。

If \(\log_{10}(x)=3.5\), then the antilogarithm gives \(x=10^{3.5}\), which is useful for converting log-scale data back to original values.
如果 \(\log_{10}(x)=3.5\),那么用反对数可得 \(x=10^{3.5}\),这在把对数刻度数据换回原始数值时很有用。

Etymology / 词源

anti-(“反、对立”)+ logarithm(“对数”)构成,字面意思是“对数的反向(运算)”。在使用对数表进行计算的时代,“antilogarithm”常用于指从对数值查回原数的过程或结果。

Related Words / 相关词

Literary Works / 文学与著作例证

  • Abramowitz & Stegun,《Handbook of Mathematical Functions》:在指数、对数与数表相关章节中常出现“antilogarithm/antilog”的用法。
  • CRC Press,《CRC Standard Mathematical Tables and Formulae》:在对数/反对数表及其应用条目中使用该术语。
  • **Press et al.**,《Numerical Recipes》:在数值计算中涉及 \(\exp(\cdot)\)、\(\log(\cdot)\) 的转换时,会出现“antilog/antilogarithm”作为口语化或说明性称呼。
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