Log[a z] == Log[a] + Log[z] /; a > 0

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

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["a_", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "a", "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], "/;", RowBox[List["a", ">", "0"]]]]]]]]

2001-10-29