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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Transformations > Power of arguments





http://functions.wolfram.com/01.04.16.0037.01









  


  








Input Form





Log[z^a] == a Log[z] /; Inequality[-Pi, Less, Im[a Log[z]], LessEqual, Pi]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mi> &#960; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ln /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <leq /> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]


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





2001-10-29