Log[a, z] Log[z, w] == Log[a, w]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> log </mi> <mi> z </mi> </msub> <mo> ( </mo> <mi> w </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <mi> w </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <log /> <logbase> <ci> a </ci> </logbase> <ci> z </ci> </apply> <apply> <log /> <logbase> <ci> z </ci> </logbase> <ci> w </ci> </apply> </apply> <apply> <log /> <logbase> <ci> a </ci> </logbase> <ci> w </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["a_", ",", "z_"]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["z_", ",", "w_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "[", RowBox[List["a", ",", "w"]], "]"]]]]]]

2001-10-29