Definition

1. Noun:
   • The antilogarithm: The number for which a given number is the logarithm. It is the inverse operation of taking a logarithm. If log_b(x) = y, then the antilog of y (with base b) is x.

Usage

• The term "antilog" is used primarily in mathematics, specifically in the context of logarithms and exponential functions. It is a shortened form of "antilogarithm."
• It is often used with a specified base (like base 10 or base ). If the base is not specified, it is commonly assumed to be 10 in many practical contexts (common logarithm).

Examples

• Noun:
  • The log of 1000 (base 10) is 3. Therefore, the antilog of 3 is 1000.
  • To find the original number, you need to take the antilog of the calculated logarithm.
  • On a calculator, the 10^x function is often used to compute the antilog for base 10.

Advanced Usage

• "Antilog" in different bases: The base is crucial. The antilog of to base is .
  • The natural log (ln) of 7.389 is approximately 2. The antilog (base e) of 2 is therefore approximately 7.389 (e^2).
• Using the term "inverse logarithm": "Antilog" is synonymous with the phrase "inverse logarithm."

Variants and Related Words

• Antilogarithm (n): The full, formal term for "antilog."
• Exponentiation (n): The general mathematical operation of raising a base to a power, which is the functional inverse of the logarithm. Finding an antilog is a specific case of exponentiation.

Synonyms

• Inverse logarithm
• Exponential (when used as a noun in context, e.g., "find the exponential")

Related Phrases / Operations

• Take the antilog: To perform the antilogarithm operation.
  • After solving the equation, take the antilog of both sides to find the value of x.
• Antilog table: A pre-calculated table used to find antilogarithms before the widespread use of calculators.
  • Students learned to use log and antilog tables for complex multiplication.

Noun

1. the number of which a given number is the logarithm