Definition

1. Noun:
   • The number corresponding to a given logarithm: The antilogarithm is the number that results when the base of a logarithm is raised to the power of a given number. If log_b(x) = y, then the antilogarithm of y (with base b) is x. It is the inverse operation of taking a logarithm.

Usage and Examples

• Noun:
  • The antilogarithm of 2, using base 10, is 100 because 10^2 = 100.
  • To find the original number, you need to calculate the antilogarithm of the logarithmic value.
  • In the equation log(500) ≈ 2.699, the antilogarithm of 2.699 is approximately 500.

Advanced Usage

• Scientific and Engineering Contexts: The term is frequently used in fields requiring logarithmic scales, such as acoustics (decibels), seismology (Richter scale), and chemistry (pH levels). Calculating the antilogarithm returns a value to its original linear scale.
  • After processing the signal in the logarithmic domain, engineers applied an antilogarithm to convert it back to a linear amplitude.

Variants and Related Words

• Antilog (n): A common abbreviated form of "antilogarithm."
  • You can find the antilog function on most scientific calculators.
• Inverse Logarithm (n): A descriptive synonym for antilogarithm.
• Exponentiation: The general mathematical operation (raising a base to a power) that finding an antilogarithm represents.

Synonyms

• Antilog: The standard shortened synonym.
• Inverse Logarithm: A descriptive synonym explaining the function.

Notes on Meaning

• The concept is inseparable from logarithms. It is not a standalone idea but is defined by its relationship as the inverse function.
• The base of the logarithm (common base 10, natural base ) is crucial. An antilogarithm is always with respect to a specific base.

Noun

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