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Fungrim entry: f67fa2

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

c \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
Loglog(z)\log(z) 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:
    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))))))

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

2021-03-15 19:12:00.328586 UTC