logarithmic function: meaning, definition, pronunciation and examples
C2Formal, Technical, Academic
Quick answer
What does “logarithmic function” mean?
A mathematical function that is the inverse of an exponential function. It is defined as f(x) = logₐ(x), where 'a' is the base.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function that is the inverse of an exponential function. It is defined as f(x) = logₐ(x), where 'a' is the base.
Any function whose output is a logarithm of its input. In broader scientific contexts, it describes processes or scales where quantities change multiplicatively, leading to rapid initial growth or decay that slows over time. The term is also used metaphorically to describe diminishing returns or perception scales (e.g., human perception of sound or light).
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. Spelling of related terms follows regional conventions (e.g., BrE 'mathematical formulae' vs. AmE 'mathematical formulas'). Pronunciation of the letter 'z' in 'logarithmic' may differ (/ˈlɒɡ.ə.rɪð.mɪk/ vs. /ˈlɔː.ɡə.rɪð.mɪk/), but this is part of general pronunciation patterns.
Connotations
Identical technical connotations. No cultural or contextual variation.
Frequency
Equally low frequency in both varieties, confined strictly to technical discourse.
Grammar
How to Use “logarithmic function” in a Sentence
The logarithmic function [of x] to the base [a]The logarithmic function [describes/graphs/models] [something][Something] follows/grows according to a logarithmic function.[Something] is transformed by a logarithmic function.Vocabulary
Collocations
Examples
Examples of “logarithmic function” in a Sentence
verb
British English
- [No standard verb form. One might say 'to logarithmically transform' the data.]
American English
- [No standard verb form. One might say 'to log-transform' the values.']
adverb
British English
- The data were plotted logarithmically.
- The response increases logarithmically with intensity.
American English
- The values scale logarithmically.
- Transform the dataset logarithmically.
adjective
British English
- The scale on the axis is logarithmic.
- We observed a logarithmic relationship between the variables.
American English
- The growth pattern is clearly logarithmic.
- Use a logarithmic scale for the y-axis.
Usage
Meaning in Context
Business
Rare. Used in advanced finance or economics to describe models of diminishing returns, utility, or logarithmic scales in charts (e.g., 'The data is plotted on a logarithmic scale').
Academic
Very common in mathematics, physics, engineering, chemistry, and computer science curricula and research. (e.g., 'Solve the equation using the properties of logarithmic functions').
Everyday
Extremely rare. Would only appear in explaining complex concepts or in specific hobbies (e.g., advanced photography discussing f-stops).
Technical
Core terminology. Used precisely to denote the specific mathematical operation or its graphical representation. (e.g., 'The sensor's response is calibrated with a logarithmic function').
Vocabulary
Synonyms of “logarithmic function”
Vocabulary
Antonyms of “logarithmic function”
Watch out
Common Mistakes When Using “logarithmic function”
- Pronouncing 'logarithmic' with a hard 'g' (as in 'go'). Correct is a soft 'g' as in 'judge'.
- Using 'logarithmic function' to describe any slow-growing process; it must have the specific mathematical form.
- Confusing 'logarithmic' (related to logs) with 'logical' (related to reason).
- Misspelling as 'logarythmic' or 'logarithmic'.
FAQ
Frequently Asked Questions
Not exactly. A 'logarithm' is a number (the result of the operation). A 'logarithmic function' is the rule or process (the function f(x) = log(x)) that produces that number for a given input.
In higher mathematics, the natural logarithmic function (base 'e', written as ln(x)) is most common. In engineering and some sciences, base 10 (written as log(x) or log₁₀(x)) is also widely used.
In precise technical language, no. 'Logarithmic growth' has a specific mathematical definition (slow growth where the rate of growth is inversely proportional to the current value). In informal metaphor, it is sometimes used, but it's best to use terms like 'very slow growth' or 'diminishing returns' in non-technical contexts.
Because for inputs just above zero, a small increase leads to a large increase in the logarithm. As the input gets very large, you need to multiply it by a large factor to increase the logarithm by the same amount, making the output increase very slowly—hence the flattening curve.
A mathematical function that is the inverse of an exponential function. It is defined as f(x) = logₐ(x), where 'a' is the base.
Logarithmic function is usually formal, technical, academic in register.
Logarithmic function: in British English it is pronounced /ˌlɒɡ.əˈrɪð.mɪk ˈfʌŋk.ʃən/, and in American English it is pronounced /ˌlɔː.ɡəˈrɪð.mɪk ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[None directly; the term is technical]”
Learning
Memory Aids
Mnemonic
Think: 'LOG' means the power you RAISE the base to. A LOGARITHMIC FUNCTION asks the question: 'What power gives me this number?' It's the inverse of an EXPONENTIAL FUNCTION, which asks: 'What number do I get when I raise the base to this power?'
Conceptual Metaphor
A COMPRESSOR or DIMINISHING RETURN: It takes large increases in input to produce small increases in output. A LAW OF DIMINISHING IMPACT.
Practice
Quiz
In which of these fields is the term 'logarithmic function' MOST precisely and commonly used?