log2fi

Log2fi is a notation that appears in some mathematical and applied texts, but it does not have a universal, single definition. In many contexts, it is used informally to denote the logarithm base 2 of a quantity labeled f_i, where f_i denotes a function, sequence, or value indexed by i. When read this way, log2fi is equivalent to log_2(f_i), and can be written as ln(f_i)/ln(2) using natural logarithms.

A precise definition depends on the meaning of f_i. If f_i is a real positive quantity, then log2fi is a real number. If f_i is not positive, the real logarithm is undefined; in such cases one may extend to the complex logarithm with an appropriate choice of branch, or restrict to a domain where f_i > 0. The notation log2fi should be read with attention to context to avoid ambiguity about what f_i represents and whether i is a subscript index or part of a function argument.

Examples illustrate the idea. If f_i = 4, then log2fi = log_2(4) = 2. If f_i = i (the imaginary unit), then log2fi = log_2(i) = (iπ/2)/ln 2 in the principal branch, yielding a complex value.

In information theory and related fields, logarithms base 2 are common because they measure information in bits. When f_i represents a frequency, probability, or other quantity, log_2 f_i often appears in entropy, coding, and divergence formulas. For clarity, many authors prefer the explicit notation log_2 f_i rather than the compact log2fi.