linguistic:translation
Logarithms

Assuming the axiom of choice and, given an infinite cardinal κ and a finite cardinal μ greater than 1, there may or may not be a cardinal λ satisfying μ λ = κ {\displaystyle \mu ^{\lambda }=\kappa }. However, if such a cardinal exists, it is infinite and less than κ, and any finite cardinality ν greater than 1 will also satisfy ν λ = κ {\displaystyle \nu ^{\lambda }=\kappa }.

The logarithm of an infinite cardinal number κ is defined as the least cardinal number μ such that κ ≤ 2. Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of cardinal invariants of topological spaces, though they lack some of the properties that logarithms of positive real numbers possess.