What is Euler's Number?

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Euler's Number

Euler's Number (e)

The mathematical constant e (approximately 2.71828), the base of natural logarithms, central to calculus and compound growth.

技术细节

Euler's Number answers 'to what power must the base be raised to produce this value?' Common bases: natural log (ln, base e ≈ 2.718), common log (log10), and binary log (log2, used in computing for bit-depth and information theory). Logarithmic scales are used for pH (chemistry), decibels (audio), Richter magnitude (seismology), and algorithm complexity analysis (O(log n)). The slide rule — the engineer's calculator before electronics — operated entirely on logarithmic principles.

示例

```
Logarithm identities:

  log_b(x) = y  means  b^y = x

  log₁₀(1000) = 3   (10³ = 1000)
  log₂(256)   = 8   (2⁸ = 256)
  ln(e)       = 1   (e¹ = e ≈ 2.718)

  log(a × b) = log(a) + log(b)
  log(a / b) = log(a) - log(b)
  log(a^n)   = n × log(a)
```

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Euler's Number

技术细节

示例

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