logarithm: meaning, definition, pronunciation and examples
C2Academic, Technical, Scientific
Quick answer
What does “logarithm” mean?
The power to which a base number must be raised to produce a given number.
Audio
Pronunciation
Definition
Meaning and Definition
The power to which a base number must be raised to produce a given number.
A mathematical function that expresses the exponent or power relationship between numbers, widely used to simplify complex calculations involving multiplication, division, exponents, and roots.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling and pronunciation are consistent.
Connotations
Connotes advanced mathematics, engineering, computer science, and scientific measurement (e.g., Richter scale, pH). Neutral technical term.
Frequency
Equally low-frequency in general discourse but standard in technical fields in both regions.
Grammar
How to Use “logarithm” in a Sentence
logarithm of (something to a base)logarithm to the base (number)log (number)Vocabulary
Collocations
Examples
Examples of “logarithm” in a Sentence
adverb
British English
- The population increased logarithmically.
American English
- The signal strength decays logarithmically with distance.
adjective
British English
- The data exhibited a logarithmic progression over time.
American English
- The sensor has a logarithmic response curve.
Usage
Meaning in Context
Business
Rare; may appear in financial modeling for calculating compound interest or in economics discussing elasticities.
Academic
Core concept in mathematics, physics, chemistry, engineering, and computer science curricula.
Everyday
Virtually never used in casual conversation.
Technical
Fundamental in algorithms, signal processing (decibels), data compression, and measuring phenomena across vast scales (e.g., earthquake magnitude, sound intensity).
Vocabulary
Synonyms of “logarithm”
Neutral
Weak
Vocabulary
Antonyms of “logarithm”
Watch out
Common Mistakes When Using “logarithm”
- Mispronouncing as 'log-a-rhythm'. Confusing 'log' (abbreviation) with 'log' as in a piece of wood. Using 'logarithm' as a verb (e.g., 'I will logarithm this' is incorrect).
FAQ
Frequently Asked Questions
'log' often denotes the common logarithm (base 10), especially in engineering, while 'ln' always denotes the natural logarithm (base e, Euler's number). In higher mathematics and computing, 'log' sometimes means the natural logarithm.
Not in the real number system. The logarithm of a negative number is a complex number.
No, the standard verb phrase is 'to take the logarithm of' or 'to compute the log of'. One does not 'logarithm' a number.
They are crucial for solving exponential equations, analyzing phenomena that span many orders of magnitude (like sound or acidity), and form the basis for efficient algorithms in computer science.
The power to which a base number must be raised to produce a given number.
Logarithm is usually academic, technical, scientific in register.
Logarithm: in British English it is pronounced /ˈlɒɡ.ə.rɪ.ðəm/, and in American English it is pronounced /ˈlɑː.ɡə.rɪ.ðəm/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “On a logarithmic scale”
- “Grows logarithmically”
Learning
Memory Aids
Mnemonic
Think 'LOG' as in a ship's log that recorded progress. A logarithm 'logs' or records the power (exponent) needed to reach a number.
Conceptual Metaphor
A COMPRESSION TOOL: Logarithms compress a wide range of numbers into a manageable scale. A TRANSLATOR: Translates the language of multiplication into the simpler language of addition.
Practice
Quiz
What is the primary purpose of a logarithm?