What is ln 2 (Natural Logarithm of 2)?

ln 2 = 1 − 1/2 + 1/3 − 1/4 + … ≈ 0.69314…
ln 2 ≈ 0.69314718055994530941. Transcendental

ln 2 is the natural logarithm of 2: the power to which e must be raised to get 2. It equals the area under the curve 1/x from x=1 to x=2. The alternating series 1 − 1/2 + 1/3 − 1/4 + … converges to exactly ln 2.

ln 2 is the half-life constant. If a quantity decays at rate k per unit time, its half-life is ln(2)/k. This governs radioactive decay, drug clearance, capacitor discharge, and population decline: any process that halves at a constant rate.

ln 2 is transcendental (a consequence of the Lindemann-Weierstrass theorem). It appears in information theory as the conversion factor between natural units (nats) and bits: 1 bit = ln 2 nats.

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