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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > General characteristics > Symmetries and periodicities > Quasi-homogeneity





http://functions.wolfram.com/01.04.04.0003.01









  


  








Input Form





Log[\[Lambda] z] == Log[\[Lambda]] + Log[z] /; \[Lambda] > 0 || \[Lambda] + z >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["\[Lambda]", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "\[Lambda]", "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]]]], "/;", " ", RowBox[List[RowBox[List["\[Lambda]", ">", "0"]], "\[Or]", " ", RowBox[List[RowBox[List["\[Lambda]", "+", "z"]], "\[GreaterEqual]", "0"]]]]]]]]








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> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#955; </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#955; </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mi> &#955; </mi> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ln /> <apply> <times /> <ci> &#955; </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> z </ci> </apply> <apply> <ln /> <ci> &#955; </ci> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <ci> &#955; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <geq /> <apply> <plus /> <ci> z </ci> <ci> &#955; </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["\[Lambda]_", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "\[Lambda]", "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["\[Lambda]", ">", "0"]], "||", RowBox[List[RowBox[List["\[Lambda]", "+", "z"]], "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29