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Fungrim entry: 4c1e1e

log ⁣(ez)=z\log\!\left({e}^{z}\right) = z
Assumptions:zCandIm(z)(π,π]z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \in \left(-\pi, \pi\right]
TeX:
\log\!\left({e}^{z}\right) = z

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \in \left(-\pi, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Loglog(z)\log(z) Natural logarithm
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
ImIm(z)\operatorname{Im}(z) Imaginary part
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("4c1e1e"),
    Formula(Equal(Log(Exp(z)), z)),
    Variables(z),
    Assumptions(And(Element(z, CC), Element(Im(z), OpenClosedInterval(Neg(Pi), Pi)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-12-30 15:00:46.909060 UTC