natural logarithm (Q1299): Difference between revisions

@@ Property / Freebase ID @@
+/m/05d2y
@@ Property / Freebase ID: /m/05d2y / rank @@
+Normal rank
@@ Property / Freebase ID: /m/05d2y / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
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-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
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@@ Property / input set @@
+set of non-negative real numbers
@@ Property / input set: set of non-negative real numbers / rank @@
+Normal rank
@@ Property / codomain @@
+set of real numbers
@@ Property / codomain: set of real numbers / rank @@
+Normal rank
@@ Property / definition domain @@
+set of positive real numbers
@@ Property / definition domain: set of positive real numbers / rank @@
+Normal rank
@@ Property / image @@
+Log.svg
@@ Property / image: Log.svg / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\ln x = \log_{e} x$ 
\ln x = \log_{\mathrm{e}} x
@@ Property / defining formula: $\ln x = \log_{e} x$ / rank @@
+Normal rank
@@ Property / defining formula: $\ln x = \log_{e} x$ / reference @@
+stated in: ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
section, verse, paragraph, or clause: 2-13.5
@@ Property / defining formula @@
+ $\ln x = \sum_{k = 1}^{\infty} \frac{z^{k}}{k} = z + \frac{z^{2}}{2} + \frac{z^{3}}{3} + \dots$ 
\ln x= \sum_{k=1}^\infty {z^k \over k} = z + {z^2 \over 2} + {z^3 \over 3} + \cdots
+Normal rank
@@ Property / MathWorld ID @@
+NaturalLogarithm
@@ Property / MathWorld ID: NaturalLogarithm / rank @@
+Normal rank
@@ Property / MathWorld ID: NaturalLogarithm / reference @@
+imported from Wikimedia project: Spanish Wikipedia
@@ Property / Encyclopædia Britannica Online ID @@
+topic/natural-logarithm
@@ Property / Encyclopædia Britannica Online ID: topic/natural-logarithm / rank @@
+Normal rank
+subject named as: natural logarithm
@@ Property / instance of @@
+type of mathematical function
@@ Property / instance of: type of mathematical function / rank @@
+Normal rank
@@ Property / instance of @@
+elementary function
@@ Property / instance of: elementary function / rank @@
+Normal rank
@@ Property / instance of @@
+logarithm
@@ Property / instance of: logarithm / rank @@
+Normal rank
@@ Property / subclass of @@
+polylogarithm
@@ Property / subclass of: polylogarithm / rank @@
+Normal rank
@@ Property / subclass of: polylogarithm / qualifier @@
+followed by: Spence's function
@@ Property / subclass of @@
+logarithm
@@ Property / subclass of: logarithm / rank @@
+Normal rank
@@ Property / OpenMath ID @@
+transc1#ln
@@ Property / OpenMath ID: transc1#ln / rank @@
+Normal rank
@@ Property / Australian Educational Vocabulary ID @@
+scot/15168
@@ Property / Australian Educational Vocabulary ID: scot/15168 / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+56017942
@@ Property / Microsoft Academic ID: 56017942 / rank @@
+Normal rank
@@ Property / Namuwiki ID @@
+자연로그
@@ Property / Namuwiki ID: 자연로그 / rank @@
+Normal rank
@@ Property / YSO ID @@
@@ Property / YSO ID: 11567 / rank @@
+Normal rank
@@ Property / YSO ID: 11567 / reference @@
+stated in: YSO-Wikidata mapping project
retrieved: 24 November 2021Timestamp +2021-11-24T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2021-11-24T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / described by source @@
+ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
+Normal rank
+section, verse, paragraph, or clause: 2-13.5
+subject named as: natural logarithm of x
@@ Property / in defining formula @@
+ $\ln x$ 
\ln x
@@ Property / in defining formula: $\ln x$ / rank @@
+Normal rank
@@ Property / in defining formula: $\ln x$ / qualifier @@
+symbol represents: natural logarithm
@@ Property / in defining formula @@
+ $\log_{a} x$ 
\log_a x
@@ Property / in defining formula: $\log_{a} x$ / rank @@
+Normal rank
@@ Property / in defining formula: $\log_{a} x$ / qualifier @@
+symbol represents: logarithm
@@ Property / OpenAlex ID @@
+C56017942
@@ Property / OpenAlex ID: C56017942 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C56017942 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / mathematical inverse @@
+natural exponential function
@@ Property / mathematical inverse: natural exponential function / rank @@
+Normal rank
@@ Property / mathematical inverse: natural exponential function / qualifier @@
+relative to: function composition
@@ Property / power series expansion @@
+ $\ln (1 + x) = \sum_{k = 1}^{\infty} \frac{(- 1)^{k - 1}}{k} x^{k} = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \dots$ 
\ln(1+x)=\sum_{k=1}^\infty \frac{(-1)^{k-1}}{k} x^k = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots
+Normal rank
@@ Property / uses @@
+Euler's number
@@ Property / uses: Euler's number / rank @@
+Normal rank
@@ Property / uses: Euler's number / qualifier @@
+criterion used: radix
@@ Property / ScienceDirect topic ID @@
+computer-science/natural-logarithm
@@ Property / ScienceDirect topic ID: computer-science/natural-logarithm / rank @@
+Normal rank
@@ Property / ScienceDirect topic ID @@
+engineering/natural-logarithm
@@ Property / ScienceDirect topic ID: engineering/natural-logarithm / rank @@
+Normal rank
@@ Property / ScienceDirect topic ID @@
+mathematics/natural-logarithm
@@ Property / ScienceDirect topic ID: mathematics/natural-logarithm / rank @@
+Normal rank
@@ Property / PlanetMath ID @@
+NaturalLogarithm
@@ Property / PlanetMath ID: NaturalLogarithm / rank @@
+Normal rank
@@ Property / PlanetMath ID @@
+ApproximationOfTheLogFunction
@@ Property / PlanetMath ID: ApproximationOfTheLogFunction / rank @@
+Normal rank
@@ Property / video @@
+Ln(x) ableiten - Logarithmusfunktionen ableiten.webm
@@ Property / video: Ln(x) ableiten - Logarithmusfunktionen ableiten.webm / rank @@
+Normal rank
@@ Property / Metamath statement ID @@
+df-log
@@ Property / Metamath statement ID: df-log / rank @@
+Normal rank

Latest revision as of 14:52, 29 July 2024

logarithm to the base of the mathematical constant e

ln x
natural logarithm function
natural logarithmic function
natural log
natural lg
ln(x)
Napierian logarithm
Naperian logarithm
logarithmus naturalis
hyperbolic logarithm

Language	Label	Description	Also known as
English	natural logarithm	logarithm to the base of the mathematical constant e	ln x natural logarithm function natural logarithmic function natural log natural lg ln(x) Napierian logarithm Naperian logarithm logarithmus naturalis hyperbolic logarithm