ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
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▼ Partial ordering relation
▼ Partially ordered set
▼ Closed interval
▼ Implicit interval partition
▼ Implicit basic real interval partition
▼ Closed real interval tagged partition
▼ Stieltjes sum
▼ Riemann sum
▼ Riemann integrable real function
▼ Real Riemann integral
Definition D865
Standard natural real logarithm function
Formulation 0
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 \frac{1}{t} \, d t \end{equation}
Formulation 1
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 \frac{dt}{t} \end{equation}
Formulation 2
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 t^{-1} \, d t \end{equation}
Children
▶ D5705: Natural real entropy function
▶ D5754: Standard real log-sum-exp function
▶ D866: Standard real logarithm function
Results
▶ R4829: Base inversion property of standard natural logarithm function
Conventions
▶
Convention 0 (Notation for standard natural basic real logarithm function)
The notation used for the D865: Standard natural real logarithm function is $x \mapsto \log(x)$ or $x \mapsto \ln(x)$.