Difference between revisions of "Relationship between logarithm (multivalued) and positive integer exponents"

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==References==
 
==References==
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of a quotient is a difference of logarithms|next=Relationship between logarithm and positive integer exponents}}: $4.1.10$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm of a quotient is a difference of logarithms|next=Relationship between logarithm and positive integer exponents}}: $4.1.10$
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 20:26, 27 June 2016

Theorem

Let $z \in \mathbb{C}$ and $n$ be a positive integer. Then the following formula holds: $$\mathrm{Log} \left( z^n \right) \subset n \mathrm{Log}(z),$$ where $\mathrm{Log}$ denotes the logarithm (multivalued) and $n \mathrm{Log}(z)=\left\{nw \colon w \in \mathrm{Log}(z)\right\}$.

Proof

References