Definition

1. Noun:
   • A mathematical concept: A logarithm is the exponent or power to which a fixed base must be raised to produce a given number. It is the inverse operation to exponentiation.

Usage

• The word "logarithm" is a countable noun. It is used in mathematical and scientific contexts to simplify calculations involving multiplication, division, and exponentiation by converting them into addition and subtraction.
• It is often abbreviated as "log".
• Common prepositions used with it are "of" (e.g., the logarithm 100) and "to the base" (e.g., logarithm 10).

Examples

• Noun:
  • The logarithm of 100 to the base 10 is 2, because 10 raised to the power of 2 equals 100.
  • Calculating the logarithm of a very large number can be done easily with a calculator.
  • Logarithms are essential tools in many fields, including acoustics and computer science.

Advanced Usage

• "Common logarithm": A logarithm with base 10, often written simply as .
  • Before calculators, common logarithms were looked up in printed tables.
• "Natural logarithm": A logarithm with base (Euler's number, approximately 2.718), written as .
  • The natural logarithm is frequently used in calculus and growth/decay models.
• "Take the logarithm of": The process of applying the logarithmic function to a number.
  • To solve the equation, you first need to take the logarithm of both sides.

Variants and Related Words

• Logarithmic (adj): Relating to or expressed in terms of logarithms.
  • The data showed a logarithmic growth pattern.
• Log (n, v): A common abbreviation for logarithm (noun). As a verb, it means to enter data into a log or to cut down trees, which is a different meaning.
  • Find the log of this value. (Here, "log" is a noun meaning logarithm).

Synonyms

• Log (noun, informal/abbreviation in mathematics).
• Exponent (This is the core concept, but "logarithm" specifically refers to the exponent in the inverse relationship).

Related Phrases and Idioms

(Note: "Logarithm" is a technical term and is not typically used in idiomatic expressions or phrasal verbs.)

Noun

1. the exponent required to produce a given number