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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Inequalities





http://functions.wolfram.com/01.04.29.0006.01









  


  








Input Form





Log[1 - Abs[x]] <= Log[1 + x] <= -Log[1 - Abs[x]] /; -1 < x < 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "x", "]"]]]], "]"]], "\[LessEqual]", RowBox[List["Log", "[", RowBox[List["1", "+", "x"]], "]"]], "\[LessEqual]", RowBox[List["-", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "x", "]"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", "x", "<", "1"]]]]]]








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> <mn> 1 </mn> <mo> - </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> x </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <cn type='integer'> -1 </cn> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "x", "]"]]]], "]"]], "\[LessEqual]", RowBox[List["Log", "[", RowBox[List["1", "+", "x"]], "]"]], "\[LessEqual]", RowBox[List["-", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "x", "]"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", "x", "<", "1"]]]]]]


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





2001-10-29