Antilog Calculators

0 calculators tagged with “Antilog”

The antilogarithm (antilog) is the inverse operation of a logarithm — it converts a logarithmic value back to the original number. If log₁₀(x) = y, then antilog₁₀(y) = 10^y = x. Antilogs are needed whenever you must reverse a log transformation: converting log-scale data back to original units, calculating H⁺ concentration from pH, finding CFU/mL from log counts, or recovering fold change from log₂ gene expression values.

All Calculators

No calculators found for this topic.

Antilog Formula

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

  • Base 10: antilog₁₀(y) = 10^y
  • Natural log: antiln(y) = e^y ≈ 2.71828^y
  • Base 2: antilog₂(y) = 2^y

Calculating Antilog Base 10

antilog₁₀(3.47) = 10^3.47
= 10³ × 10^0.47 = 1000 × 2.951 = 2,951

On a calculator: enter the value, press 10^x or INV LOG.

Calculating Natural Antilog

antiln(2.5) = e^2.5 ≈ 12.18

On a calculator: enter the value, press e^x or INV LN.

Applications

pH → H⁺ Concentration

pH = −log₁₀[H⁺] → [H⁺] = 10^(−pH)
pH 5.3 → [H⁺] = 10^(−5.3) = 5.0 × 10⁻⁶ mol/L

Microbiology: Log CFU → CFU/mL

Log₁₀(CFU/mL) = 6.8 → CFU/mL = 10^6.8 = 6.31 × 10⁶

Gene Expression: Log₂ Fold Change

log₂(FC) = 2.3 → FC = 2^2.3 = 4.93-fold

Quick Reference

  • antilog₁₀(0) = 1; antilog₁₀(1) = 10; antilog₁₀(2) = 100
  • antilog₁₀(0.5) ≈ 3.16; antilog₁₀(−1) = 0.1
  • antiln(0) = 1; antiln(1) ≈ 2.718; antiln(−1) ≈ 0.368

Glossary

Antilogarithm (Antilog)
The inverse of a logarithm. Antilog_b(y) = b^y. For base 10: 10^y. For natural log: e^y. Converts a logarithmic value back to the original number.
10^x Function
The base-10 exponential — antilogarithm of common (base 10) logarithms. Found on calculators as the 10^x or INV LOG button. Used to reverse log₁₀ transformations.
e^x (Natural Exponential)
The antilogarithm of natural logarithms. e ≈ 2.71828. Found on calculators as e^x or INV LN. Used to reverse ln transformations in growth equations, thermodynamics, and statistics.

Frequently Asked Questions

Antilog_b(y) = b^y. For base 10: antilog₁₀(y) = 10^y. For natural log: antiln(y) = e^y. For base 2: antilog₂(y) = 2^y. On a calculator, use the 10^x or INV LOG button (base 10) and e^x or INV LN (natural log). The antilog reverses the logarithm — if log₁₀(x) = 3.5, then x = 10^3.5 = 3,162.

Since pH = −log₁₀[H⁺], rearranging gives [H⁺] = 10^(−pH). This is the base-10 antilog of negative pH. pH 7 → [H⁺] = 10⁻⁷ = 1 × 10⁻⁷ mol/L. pH 4 → [H⁺] = 10⁻⁴ = 1 × 10⁻⁴ mol/L. Each whole unit change in pH = a 10-fold change in H⁺ concentration.

For any base b: antilog_b(0) = b⁰ = 1. This is because log_b(1) = 0 for any base — any base raised to the zero power equals 1. The antilog reverses this: antilog(0) = 1. For base 10: 10⁰ = 1. For natural log: e⁰ = 1.

Microbiology data (bacterial colony counts, viral titers) are often expressed on a log₁₀ scale because values span many orders of magnitude. To convert back to actual counts: CFU/mL = 10^(log₁₀ CFU/mL). For example, a sample with log₁₀ count = 5.7 contains 10^5.7 = 5.01 × 10⁵ CFU/mL. Serial dilution results and dose-response curves are routinely plotted on log scales and require antilog conversion for concentration calculations.