logarithm

IPA/ˈlɒɡərɪðəm/
KK[lˈɑɡɚˌɪðəm]IPA/ˈlɔːɡərɪðəm/

logarithm — noun

  • logarithmsingular
  • logarithmsplural

1. a number that tells you what power a base must be raised to in order to make ano

1.nounC1
Definition

a number that tells you what power a base must be raised to in order to make another number.

Example

In class, Roya showed that the logarithm of 100 is 2 in base 10.

pattern: logarithm of X in base 10

On the worksheet, Liam had to find the logarithm of 64 to base 2.

pattern: logarithm of X to base Y

Common collocations
  • natural logarithm
  • common logarithm
  • logarithm table
  • find the logarithm
Synonyms
  • log

    an informal short form often used in formulas, textbooks, and computing

  • log value

    a technical phrase for the numerical result rather than the full concept

Grammar Patterns

the logarithm of [number]

the logarithm of [number] to base [number]

natural/common logarithm

Usage Note

Usually appears in maths or science contexts with a base named directly or understood from context. Distinguish from an exponent: the exponent is the power written in an expression, while the logarithm is the power you need to reach a chosen number.

Common Mistakes

The logarithm of 100 to base 10 is 100.
The logarithm of 100 to base 10 is 2.
the logarithm is the power you need, not the original number.

Word family

Synonym discussion

Sense: noun/1

Logarithm, exponent, power, and ratio all appear in maths, but they do different jobs. A logarithm tells you which power of a base gives a chosen number, so it works backward from the result. Exponent and power usually name the raised number itself in an expression such as 2^5. Ratio compares two amounts rather than describing repeated multiplication. In class, you might say 'the exponent is 5' when reading 2^5, but 'the logarithm of 32 to base 2 is 5' when solving the reverse question. Think of logarithm as the answer to 'what power do I need?', not just any number in a formula.

logarithm ↗exponent ↗power ↗ratio ↗

Common collocations

Nouns

Adverbs

Phrases

  • the logarithm of X
  • to base 10
  • natural logarithm
  • common logarithm

Prepositions

Etymology

GreekNeo-LatinFrenchEnglish

Logarithm was built in early modern science from Greek parts meaning 'word or reason' and 'number'. Scholars first shaped it in Neo-Latin, then French passed it into English. The name reflects the idea of turning difficult multiplication into a simpler number-based calculation.