Fungrim entry: f67fa2

\log\!\left(c z\right) = \log(c) + \log(z)

Assumptions:

c \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

\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\}

Definitions:

Fungrim symbol	Notation	Short description
`Log`	$\log(z)$	Natural logarithm
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	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

Natural logarithm

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