common logarithm: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “common logarithm” mean?
A logarithm with base 10. It is the exponent to which 10 must be raised to produce a given number.
Audio
Pronunciation
Definition
Meaning and Definition
A logarithm with base 10. It is the exponent to which 10 must be raised to produce a given number. Written as log₁₀(x) or simply log(x).
Historically the most widely used logarithm in calculations, engineering, and science before the advent of computers, due to the decimal number system. It is used to measure quantities that span many orders of magnitude, such as sound intensity (decibels) and earthquake strength (Richter scale).
Dialectal Variation
British vs American Usage
Differences
Usage is identical in technical meaning. The potential difference lies in educational emphasis; historically, UK syllabuses sometimes introduced Napierian logarithms (ln) earlier alongside common logarithms.
Connotations
Neutral and precise in both varieties.
Frequency
High frequency in mathematics, engineering, and physical sciences textbooks and literature in both regions.
Grammar
How to Use “common logarithm” in a Sentence
The common logarithm of [number] is [value].To find/calculate [result], take the common logarithm of [input].Vocabulary
Collocations
Examples
Examples of “common logarithm” in a Sentence
noun
British English
- The common logarithm is essential for interpreting the Richter scale.
- He consulted a book of common logarithms for the calculation.
American English
- The pH calculation requires taking the common logarithm of the hydrogen ion concentration.
- Engineers often use common logarithms for gain measurements in decibels.
Usage
Meaning in Context
Business
Rare, except in highly technical financial modelling involving logarithmic scales or decibels in corporate telecoms.
Academic
Core concept in mathematics, physics, chemistry, and engineering courses. Used in formulas, data analysis on logarithmic plots, and understanding scales like pH or Richter.
Everyday
Virtually never used.
Technical
The primary domain. Used in scientific calculators, computer functions (LOG), signal processing, and acoustics.
Vocabulary
Synonyms of “common logarithm”
Vocabulary
Antonyms of “common logarithm”
Watch out
Common Mistakes When Using “common logarithm”
- Writing 'log(x)' and assuming it's always base 10 without confirming the context (in many programming languages and advanced maths, 'log' is base e).
- Forgetting the base when solving logarithmic equations: log(x) = 2 implies x = 100 only if the base is 10.
- Confusing the common logarithm (log₁₀) with the natural logarithm (ln or logₑ).
FAQ
Frequently Asked Questions
On most basic and scientific calculators, the 'log' button is for the common logarithm (base 10). The 'ln' button is for the natural logarithm (base e).
It's called 'common' because it uses base 10, which is the base of our common decimal number system, making it historically the most frequently used logarithm for calculation.
'log' (without a specified base) often, but not always, means the common logarithm (base 10), especially in engineering and secondary education. 'ln' always means the natural logarithm (base e, where e ≈ 2.718). In higher mathematics, 'log' can sometimes mean the natural logarithm, so context is key.
You encounter them indirectly through scales that use them: the Richter scale for earthquakes, the decibel scale for sound, the pH scale for acidity, and the magnitude scale for stellar brightness.
A logarithm with base 10. It is the exponent to which 10 must be raised to produce a given number.
Common logarithm is usually technical / academic in register.
Common logarithm: in British English it is pronounced /ˌkɒm.ən ˈlɒɡ.ə.rɪ.ðəm/, and in American English it is pronounced /ˌkɑː.mən ˈlɑː.ɡə.rɪ.ðəm/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
COMMON logarithm is your COMMON, everyday base-10 log, just like our COMMON decimal system. Think of 'common' as meaning 'shared by the decimal system'.
Conceptual Metaphor
A MEASURING STICK FOR ORDERS OF MAGNITUDE. It compresses vast numerical ranges into a manageable scale, acting as a gauge for 'how many tens' are multiplied together.
Practice
Quiz
In which of these fields is the common logarithm MOST frequently applied?