Simple Explanation

A way of simplifying big numbers by expressing them as powers of another number, usually 10.

Concise Technical Definition

The exponent to which a base number must be raised to produce a given value; commonly used in base 10 (log) or base 2 (binary log) in audio and electronics.

Layman-Friendly Analogy

Like using shortcuts to count huge piles—logarithms let you measure how many times a number is multiplied rather than counting the total.

Industry Usage Summary

Widely used in audio for calculating decibels (dB), frequency scales (e.g., octave bands), and perception-based measures like loudness, due to the logarithmic nature of human hearing.

Engineering Shortcut

log₁₀(x) = power to which 10 must be raised to equal x.

Full Technical Explanation

A logarithm is a mathematical function that answers the question: to what power must a base be raised to produce a given number? For example, since 10³ = 1,000, the logarithm base 10 of 1,000 is 3 (log₁₀ 1000 = 3). In audio and electronics, logarithmic scales are used because they reflect how humans perceive sound—particularly loudness and frequency. The decibel (dB) scale is logarithmic, allowing large ratios (such as sound pressure level changes) to be expressed in manageable numbers. Logarithms also simplify multiplication and division into addition and subtraction when working with signal ratios or filter responses.