U+33D1 was added to Unicode in version 1.1 (1993). It belongs to the block CJK Compatibility in the 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 . 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 Wikipedia has the following information about this codepoint:

The

natural logarithmof a number is its logarithm to the basee, whereeis an irrational and transcendental constant approximately equal to 7000271828182845899♠2.718281828459. The natural logarithm ofxis generally written as lnx, log_{e}x, or sometimes, if the baseeis implicit, simply logx. Parentheses are sometimes added for clarity, giving ln(x), log_{e}(x) or log(x). This is done in particular when the argument to the logarithm is not a single symbol, to prevent ambiguity.The natural logarithm of

xis the power to whichewould have to be raised to equalx. For example, ln(7.5) is 2.0149..., becausee^{2.0149...}= 7.5. The natural log ofeitself, ln(e), is 1, becausee^{1}=e, while the natural logarithm of 1, ln(1), is 0, sincee^{0}= 1.The natural logarithm can be defined for any positive real number

aas the area under the curvey= 1/xfrom 1 toa(the area being taken as negative whena<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 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.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:

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

Thus, the logarithm function is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition, represented as a function:

Logarithms can be defined to 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 are usually defined in terms of the latter. For instance, the binary logarithm is the natural logarithm divided by ln(2), the natural logarithm of 2. 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 the sciences and are used in finance to solve problems involving compound interest.

System | Representation |
---|---|

Nº | 13265 |

UTF-8 | E3 8F 91 |

UTF-16 | 33 D1 |

UTF-32 | 00 00 33 D1 |

URL-Quoted | %E3%8F%91 |

HTML-Escape | ㏑ |

Wrong windows-1252 Mojibake | ã |

Property | Value |
---|---|

Age (age) | 1.1 |

Unicode Name (na) | SQUARE LN |

Unicode 1 Name (na1) | SQUARED LN |

Block (blk) | CJK_Compat |

General Category (gc) | Other Symbol |

Script (sc) | Common |

Bidirectional Category (bc) | Left To Right |

Combining Class (ccc) | Not Reordered |

Decomposition Type (dt) | Square |

Decomposition Mapping (dm) | |

Lowercase (Lower) | ✘ |

Simple Lowercase Mapping (slc) | |

Lowercase Mapping (lc) | |

Uppercase (Upper) | ✘ |

Simple Uppercase Mapping (suc) | |

Uppercase Mapping (uc) | |

Simple Titlecase Mapping (stc) | |

Titlecase Mapping (tc) | |

Case Folding (cf) | |

ASCII Hex Digit (AHex) | ✘ |

Alphabetic (Alpha) | ✘ |

Bidi Control (Bidi_C) | ✘ |

Bidi Mirrored (Bidi_M) | ✘ |

Bidi Paired Bracket (bpb) | |

Bidi Paired Bracket Type (bpt) | None |

Cased (Cased) | ✘ |

Composition Exclusion (CE) | ✘ |

Case Ignorable (CI) | ✘ |

Full Composition Exclusion (Comp_Ex) | ✘ |

Changes When Casefolded (CWCF) | ✘ |

Changes When Casemapped (CWCM) | ✘ |

Changes When NFKC Casefolded (CWKCF) | ✔ |

Changes When Lowercased (CWL) | ✘ |

Changes When Titlecased (CWT) | ✘ |

Changes When Uppercased (CWU) | ✘ |

Dash (Dash) | ✘ |

Deprecated (Dep) | ✘ |

Default Ignorable Code Point (DI) | ✘ |

Diacritic (Dia) | ✘ |

East Asian Width (ea) | Wide |

Extender (Ext) | ✘ |

FC NFKC Closure (FC_NFKC) | |

Grapheme Cluster Break (GCB) | Any |

Grapheme Base (Gr_Base) | ✔ |

Grapheme Extend (Gr_Ext) | ✘ |

Grapheme Link (Gr_Link) | ✘ |

Hex Digit (Hex) | ✘ |

Hangul Syllable Type (hst) | Not Applicable |

Hyphen (Hyphen) | ✘ |

ID Continue (IDC) | ✘ |

Ideographic (Ideo) | ✘ |

ID Start (IDS) | ✘ |

IDS Binary Operator (IDSB) | ✘ |

IDS Trinary Operator and (IDST) | ✘ |

InMC (InMC) | — |

Indic Positional Category (InPC) | NA |

Indic Syllabic Category (InSC) | Other |

ISO 10646 Comment (isc) | — |

Joining Group (jg) | No_Joining_Group |

Join Control (Join_C) | ✘ |

Jamo Short Name (JSN) | — |

Joining Type (jt) | Non Joining |

Line Break (lb) | Ideographic |

Logical Order Exception (LOE) | ✘ |

Math (Math) | ✘ |

Noncharacter Code Point (NChar) | ✘ |

NFC Quick Check (NFC_QC) | Yes |

NFD Quick Check (NFD_QC) | Yes |

NFKC Casefold (NFKC_CF) | |

NFKC Quick Check (NFKC_QC) | No |

NFKD Quick Check (NFKD_QC) | No |

Numeric Type (nt) | None |

Numeric Value (nv) | NaN |

Other Alphabetic (OAlpha) | ✘ |

Other Default Ignorable Code Point (ODI) | ✘ |

Other Grapheme Extend (OGr_Ext) | ✘ |

Other ID Continue (OIDC) | ✘ |

Other ID Start (OIDS) | ✘ |

Other Lowercase (OLower) | ✘ |

Other Math (OMath) | ✘ |

Other Uppercase (OUpper) | ✘ |

Pattern Syntax (Pat_Syn) | ✘ |

Pattern White Space (Pat_WS) | ✘ |

Quotation Mark (QMark) | ✘ |

Radical (Radical) | ✘ |

Sentence Break (SB) | Other |

Simple Case Folding (scf) | |

Script Extension (scx) | Common |

Soft Dotted (SD) | ✘ |

STerm (STerm) | ✘ |

Terminal Punctuation (Term) | ✘ |

Unified Ideograph (UIdeo) | ✘ |

Variation Selector (VS) | ✘ |

Word Break (WB) | Other |

White Space (WSpace) | ✘ |

XID Continue (XIDC) | ✘ |

XID Start (XIDS) | ✘ |

Expands On NFC (XO_NFC) | ✘ |

Expands On NFD (XO_NFD) | ✘ |

Expands On NFKC (XO_NFKC) | ✔ |

Expands On NFKD (XO_NFKD) | ✔ |