Mathematics July 22, 2026 · 10 min read

Antilogarithms: The Inverse Operation That Completes the Logarithm

Understand antilogarithms with formulas, worked examples, and applications in pH calculations, decibels, and compound interest.

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The antilogarithm (antilog) is the inverse operation of the logarithm. If a logarithm asks "what power must I raise the base to get this number?", the antilog answers "what number do I get when I raise the base to this power?"

The Formula

If log_b(x) = y, then antilog_b(y) = b^y = x

Worked Example

Find the antilog of 2.5 (base 10):

  1. antilog₁₀(2.5) = 10^2.5
  2. = 10² × 10^0.5
  3. = 100 × 3.16228 ≈ 316.228

Applications

  • pH calculations: [H⁺] = 10^(-pH)
  • Decibels: Power ratio = 10^(dB/10)
  • Richter scale: Magnitude = 10^(value)