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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[a,z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.05.16.0011.01









  


  








Input Form





Log[a, Subscript[z, 1]] - Log[a, Subscript[z, 2]] == Log[a, Subscript[z, 1]/Subscript[z, 2]] /; Subscript[z, 2] - Subscript[z, 1] >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["a", ",", SubscriptBox["z", "1"]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["a", ",", SubscriptBox["z", "2"]]], "]"]]]], "\[Equal]", RowBox[List["Log", "[", RowBox[List["a", ",", FractionBox[SubscriptBox["z", "1"], RowBox[List[" ", SubscriptBox["z", "2"]]]]]], "]"]]]], "/;", " ", RowBox[List[RowBox[List[SubscriptBox["z", "2"], "-", SubscriptBox["z", "1"]]], "\[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> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <log /> <logbase> <ci> a </ci> </logbase> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <log /> <logbase> <ci> a </ci> </logbase> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <log /> <logbase> <ci> a </ci> </logbase> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <geq /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["a_", ",", SubscriptBox["z_", "1"]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["a_", ",", SubscriptBox["z_", "2"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", RowBox[List["a", ",", FractionBox[SubscriptBox["zz", "1"], SubscriptBox["zz", "2"]]]], "]"]], "/;", RowBox[List[RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]], "\[GreaterEqual]", "0"]]]]]]]]


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





2001-10-29