Functions and operators\ln

\lnCommand

Used for the natural logarithm in calculus, analysis, and applied mathematics

\ln
Available in
base, physics
Kind
prefix
Allowed mode
math
Frequency
1.42% of corpus formulasrank 41 of 263
Commonality
high
Renderer support
PackageMathJaxKaTeXXeTeX
baseMathJax: FullKaTeX: FullXeTeX: Full
physicsMathJax: FullKaTeX: FullXeTeX: Full
About the test scope

Syntax#

\ln

Takes no arguments. In base. Reading argspecs

\lno[a]optional math contentd()(b)optional math content

Argspec o d() — two optional arguments. In physics. Reading argspecs

Common tasks#

How to write a natural logarithm#

\ln x

How to write the log of a product#

\ln(ab)=\ln a+\ln b

How to write a change-of-base identity#

\ln x = \frac{\log x}{\log e}

Examples#

physics

\ln x

physics

\ln[2](x)

Package variants#

PackageSignatureAllowed modeNotes
basemathUsed for the natural logarithm in calculus, analysis, and applied mathematics
physicso d()mathUsed for natural-logarithm notation, including optional bracketed powers such as \ln[2](x) in the physics package.

In TeXForm#

TeXForm parses this entry as prefix syntax; the package determines its argument specification.

physics/named-fn-paren-expandfrom Faithfulreading

Expand physics power and auto-sized parenthesis arguments of standard named functions.

\sin(#1) \sin\left(#1\right)

See also#

Test cases#

base
InputCaseMathJaxKaTeXXeTeX
\lnPositive · baselinePassPassPass
physics
InputCaseMathJaxKaTeXXeTeX
\lnPositive · baselinePassPassPass
\ln[a]Positive · vary:o[0]PassPassPass
\ln (a)Positive · vary:d[1]PassPassPass
\ln[a](b)Positive · maximalPassPassPass
All 74 in Functions and operators