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.
التفاصيل التقنية
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.
مثال
``` 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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