Log[-1, z] == -((I Log[z])/Pi)

Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", "z", "]"]]]], "\[Pi]"]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> log </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mi> &#960; </mi> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <log /> <logbase> <cn type='integer'> -1 </cn> </logbase> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", "z", "]"]]]], "\[Pi]"]]]]]]]

2001-10-29