Difference between revisions of "Logarithm of product is a sum of logarithms"
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| + | ==Theorem== | ||
| + | Let $z_1,z_2 \in \mathbb{C}$ such that $-\pi < \mathrm{arg}(z_1) + \mathrm{arg}(z_2) \leq \pi$. Then the following formula holds: | ||
| + | $$\log(z_1z_2) = \log(z_1)+\log(z_2),$$ | ||
| + | where $\log$ denotes the [[logarithm]]. | ||
| + | |||
| + | ==Proof== | ||
| + | |||
==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm (multivalued) of product is a sum of logarithms (multivalued)|next=}}: 4.1.7 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm (multivalued) of product is a sum of logarithms (multivalued)|next=Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued)}}: 4.1.7 |
Revision as of 06:16, 4 June 2016
Theorem
Let $z_1,z_2 \in \mathbb{C}$ such that $-\pi < \mathrm{arg}(z_1) + \mathrm{arg}(z_2) \leq \pi$. Then the following formula holds: $$\log(z_1z_2) = \log(z_1)+\log(z_2),$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.7
