Sigmoid Function
An S-shaped function mapping any real number to a value between 0 and 1, widely used in logistic regression and neural networks.
Chi tiết kỹ thuật
Sigmoid Function 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.
Ví dụ
``` 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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