Log[z] == Limit[(z^\[Epsilon] - 1)/\[Epsilon], \[Epsilon] -> 0]

Cell[BoxData[RowBox[List[RowBox[List["Log", "[", "z", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "\[Epsilon]"], "-", "1"]], "\[Epsilon]"], ",", RowBox[List["\[Epsilon]", "\[Rule]", "0"]]]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#1013; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mfrac> <mrow> <msup> <mi> z </mi> <mi> &#1013; </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> &#1013; </mi> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ln /> <ci> z </ci> </apply> <apply> <limit /> <bvar> <ci> &#1013; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#1013; </ci> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <ci> &#1013; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> &#1013; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "\[Epsilon]"], "-", "1"]], "\[Epsilon]"], ",", RowBox[List["\[Epsilon]", "\[Rule]", "0"]]]], "]"]]]]]]

2001-10-29