log2i1

Log2i1 is a compact notation used to denote the binary logarithm of the quantity i1. In mathematics and computer science, the logarithm base 2 of a positive quantity x is written log2 x or log_2 x; log2i1 is a shorthand form when the argument is clearly i1. The variable i1 is typically a positive real number, often an index or value arising from a sequence or data set.

Computation and properties: The value is defined for i1 > 0. It can be computed as ln(i1) / ln(2). It is a monotone increasing function of i1; if i1 is a power of two, log2i1 is an integer equal to the exponent. The derivative with respect to i1 is 1 / (i1 ln 2) for i1 > 0. For i1 in the positive integers, log2i1 captures the position of i1 on a binary scale.

Examples and applications: If i1 = 1, log2i1 = 0; i1 = 2 yields 1; i1 = 3 yields about 1.585. In computer science and information theory, the binary logarithm relates to the number of bits needed to represent i1 in binary, approximately floor(log2 i1) + 1. It also appears in algorithmic time complexity analyses, data encoding, and measures of information where binary scaling is relevant.

Notes and alternatives: In strictly formal writing, log_2(i1) is often preferred; log2(i1) may be used in informal contexts. If i1 can be zero or negative, the real-valued log is undefined; complex extensions exist but are not standard in introductory discussions of log2i1. See also logarithm, binary logarithm, and bit length.