log

Log is a term with multiple meanings across disciplines. It can refer to a solid section of a tree trunk or a cut piece of timber; a written record such as a logbook or a computer log file; or the mathematical logarithm, which is the inverse of exponentiation. It can also function as a verb meaning to record information or to cut down trees.

In forestry and carpentry, a log is a segment of a tree trunk that has been felled or peeled and measured by length and diameter. Logs are processed into boards, beams, pulp, or engineered products. The moisture content and species influence their value and use.

In mathematics, the logarithm base b of x is the exponent to which b must be raised to yield x. Notation includes log_b(x). Common logarithms use base 10; natural logarithms use base e; binary logarithms use base 2. Key rules include log_b(xy) = log_b(x) + log_b(y) and log_b(x^k) = k log_b(x). The change-of-base formula is log_b(x) = log_k(x) / log_k(b). Examples: log_10(1000) = 3; ln(e) = 1.

In computing and navigation contexts, a log is a record of events. A log file on a computer stores timestamps and messages for software operation, debugging, or auditing; log management often includes rotation, archival, and filtering by severity levels such as debug, info, warning, and error. A logbook records a voyage, flight, or other activities.

The term also appears in phrases such as log scale, which uses logarithmic spacing to handle large ranges of values, and in the general practice of logging, meaning to record or to fell trees for timber.