Home U+3300 to U+33FF CJK Compatibility

# U+33D1Square Ln

U+33D1 was added to Unicode in version 1.1 (1993). It belongs to the block U+3300 to U+33FF CJK Compatibility in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Other Symbol and is commonly used, that is, in no specific script.

The glyph is a Square composition of the glyphs Latin Small Letter L, Latin Small Letter N. It has a Wide East Asian Width. In bidirectional context it acts as Left To Right and is not mirrored. In text U+33D1 behaves as Ideographic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln 7.5 is 2.0149..., because e2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1.

The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural". The definition of the natural logarithm can then be extended to give logarithm values for negative numbers and for all non-zero complex numbers, although this leads to a multi-valued function: see Complex logarithm for more.

The natural logarithm function, if considered as a real-valued function of a real variable, is the inverse function of the exponential function, leading to the identities:

e ln ⁡ x = x  if  x  is strictly positive  , ln ⁡ e x = x  if  x  is any real number . {displaystyle {egin{aligned}e^{ln x}&=xqquad { ext{ if }}x{ ext{ is strictly positive }},\ln e^{x}&=xqquad { ext{ if }}x{ ext{ is any real number .}}end{aligned}}}

Like all logarithms, the natural logarithm maps multiplication of positive numbers into addition:

ln ⁡ ( x ⋅ y ) = ln ⁡ x + ln ⁡ y   . {displaystyle ln(xcdot y)=ln x+ln y~.}

Logarithms can be defined for any positive base other than 1, not only e. However, logarithms in other bases differ only by a constant multiplier from the natural logarithm, and can be defined in terms of the latter. For instance, the base-2 logarithm (also called the binary logarithm) is equal to the natural logarithm divided by ln(2), the natural logarithm of 2, or equivalently, multiplied by log2(e).

Logarithms are useful for solving equations in which the unknown appears as the exponent of some other quantity. For example, logarithms are used to solve for the half-life, decay constant, or unknown time in exponential decay problems. They are important in many branches of mathematics and scientific disciplines, and are used to solve problems involving compound interest.

## Representations

System Representation
13265
UTF-8 E3 8F 91
UTF-16 33 D1
UTF-32 00 00 33 D1
URL-Quoted %E3%8F%91
HTML hex reference &#x33D1;
Wrong windows-1252 Mojibake ã‘

## Complete Record

Property Value
Age 1.1 (1993)
Unicode Name SQUARE LN
Unicode 1 Name SQUARED LN
Block CJK Compatibility
General Category Other Symbol
Script Common
Bidirectional Category Left To Right
Combining Class Not Reordered
Decomposition Type Square
Decomposition Mapping Latin Small Letter L Latin Small Letter N
Lowercase
Simple Lowercase Mapping Square Ln
Lowercase Mapping Square Ln
Uppercase
Simple Uppercase Mapping Square Ln
Uppercase Mapping Square Ln
Simple Titlecase Mapping Square Ln
Titlecase Mapping Square Ln
Case Folding Square Ln
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Composition Exclusion
Case Ignorable
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Cased
Full Composition Exclusion
Default Ignorable Code Point
Dash
Deprecated
Diacritic
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji Presentation
Emoji
Extender
Extended Pictographic
FC NFKC Closure Square Ln
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
Ideographic
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
Jamo Short Name
Join Control
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Latin Small Letter L Latin Small Letter N
NFKC Quick Check No
NFKD Quick Check No
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Prepended Concatenation Mark
Pattern Syntax
Pattern White Space
Quotation Mark
Regional Indicator
Sentence Break Other
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Square Ln
Bidi Paired Bracket Type None
East Asian Width Wide
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Non Joining
Line Break Ideographic
Numeric Type None
Numeric Value not a number
Simple Case Folding Square Ln
Script Extension
Vertical Orientation U