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Fungrim entry: f67fa2

log ⁣(cz)=log ⁣(c)+log ⁣(z)\log\!\left(c z\right) = \log\!\left(c\right) + \log\!\left(z\right)
Assumptions:c(0,)andzC{0}c \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\log\!\left(c z\right) = \log\!\left(c\right) + \log\!\left(z\right)

c \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f67fa2"),
    Formula(Equal(Log(Mul(c, z)), Add(Log(c), Log(z)))),
    Variables(c, z),
    Assumptions(And(Element(c, OpenInterval(0, Infinity)), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

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

2019-09-15 11:00:55.020619 UTC