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The 18 pages that link to Natural logarithm, each with the reason it gives.

• Prime number theoremRelated: Its growth rate sets the scale of the theorem's estimate for prime density.

• Exponential growthRelated: Taking natural logarithms turns an exponential relationship into a linear one.

• Logarithmic scaleRelated: It uses a different numerical unit for scale positions while preserving equal-ratio spacing.

• Exponential decayRelated: Taking logarithms turns an exponential decay curve into a straight line.

• Van ’t Hoff equationRelated: The integrated equation makes the logarithm of the equilibrium constant linear in reciprocal temperature.

• AntiderivativeRelated: It supplies a standard antiderivative for reciprocal functions on positive intervals.

• Euler's NumberRelated: It is the logarithm whose base is this constant.

• Alternating harmonic seriesRelated: The series’ exact sum is the natural logarithm of two.

• Euler–Mascheroni constantRelated: Subtracting ln n from the nth harmonic number produces the sequence converging to γ.

• Logarithmic differentiationRelated: Its derivative, 1/x, makes differentiating the logarithm of a positive function especially direct.

• Law of the iterated logarithmRelated: The iterated logarithm is log(log n), which grows slowly enough to expose long-run extremes.

• NeperRelated: The neper measures a field-quantity ratio by taking this logarithm.

• Carleman's inequalityRelated: Taking logarithms turns products in geometric means into sums.

• Gibbs' inequalityRelated: The log ratio in the inequality conventionally uses this logarithm, measured in nats.