Log[a, z] \[Proportional] Log[z]/Log[a] /; (z -> 0 | Infinity)

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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> &#8733; </mo> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mn> 0 </mn> <mo> | </mo> <mi> &#8734; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <log /> <logbase> <ci> a </ci> </logbase> <ci> z </ci> </apply> <apply> <times /> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <ci> Alternatives </ci> <cn type='integer'> 0 </cn> <infinity /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29