![]() ![]() Every family of sets with n different sets has at least log 2 n elements in its union, with equality when the family is a power set.Relatedly, the Strahler number of a river system with n tributary streams is at most log 2 n + 1. Every binary tree with n leaves has height at least log 2 n, with equality when n is a power of two and the tree is a complete binary tree.The height of the tree (number of rounds of the tournament) is the binary logarithm of the number of players, rounded up to an integer.Īlthough the natural logarithm is more important than the binary logarithm in many areas of pure mathematics such as number theory and mathematical analysis, the binary logarithm has several applications in combinatorics: Combinatorics A 16-player single elimination tournament bracket with the structure of a complete binary tree. However, the natural logarithm and the nat are also used in alternative notations for these definitions. With these units, the Shannon–Hartley theorem expresses the information capacity of a channel as the binary logarithm of its signal-to-noise ratio, plus one. In information theory, the definition of the amount of self-information and information entropy is often expressed with the binary logarithm, corresponding to making the bit the fundamental unit of information. In mathematics, the binary logarithm ( log 2 n) is the power to which the number 2 must be raised to obtain the value n. Graph of log 2 x as a function of a positive real number x ![]()
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