Exponential function: Representations through equivalent functions (formula 01.03.27.0024)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Representations through equivalent functions

With related functions

Involving power function

http://functions.wolfram.com/01.03.27.0024.01

Input Form

E^z == w^a /; a == z/Log[w]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", SuperscriptBox["w", "a"]]], "/;", RowBox[List["a", "\[Equal]", FractionBox["z", RowBox[List["Log", "[", "w", "]"]]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⩵ </mo> <msup> <mi> w </mi> <mi> a </mi> </msup> </mrow> <mo> /; </mo> <mrow> <mi> a </mi> <mo> ⩵ </mo> <mfrac> <mi> z </mi> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> w </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <ci> w </ci> <ci> a </ci> </apply> </apply> <apply> <eq /> <ci> a </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <ln /> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["w", "a"], "/;", RowBox[List["a", "\[Equal]", FractionBox["z", RowBox[List["Log", "[", "w", "]"]]]]]]]]]]]

Date Added to functions.wolfram.com (modification date)

2007-05-02