Antilog Calculator — Inverse Logarithm Calculator
Calculate the antilogarithm (inverse log) of any number with any base. If logb(x) = y, then antilogb(y) = x = by. Essential for mathematics, science, and engineering calculations. See also our Logarithm Calculator and Exponents Calculator.
antilog10(3) = 103 =
1000
How to Calculate Antilog
- Enter the antilog number (the exponent value y).
- Enter the base value (default is 10 for common antilog).
- Click Calculate to get the result.
- The result is b raised to the power y: antilogb(y) = by.
Antilog Formula
Antilogarithm Definition:
If log_b(x) = y, then antilog_b(y) = x = b^y
Common Antilog (base 10):
antilog₁₀(y) = 10^y
Example: antilog₁₀(3) = 10³ = 1000
Natural Antilog (base e):
antilog_e(y) = e^y = exp(y)
Example: antilog_e(1) = e¹ = 2.71828...
Binary Antilog (base 2):
antilog₂(y) = 2^y
Example: antilog₂(8) = 2⁸ = 256
General Formula:
antilog_b(y) = b^y
Where: b = base, y = logarithm value
Relationship:
log_b(x) = y ⟺ antilog_b(y) = x
log and antilog are inverse functionsExample Calculation
Problem: Find antilog₁₀(2.5)
Given: y = 2.5, base = 10
Solution: antilog₁₀(2.5) = 10^2.5 = 10² × 10^0.5 = 100 × 3.16228 = 316.228
Answer: antilog₁₀(2.5) = 316.2278
Technical Details
The antilogarithm is the inverse function of the logarithm. While a logarithm answers "what power must I raise the base to in order to get x?", the antilogarithm answers "what number do I get when I raise the base to this power?". In mathematical notation, if logb(x) = y, then antilogb(y) = by = x.
Antilogarithms are widely used in science and engineering. In chemistry, pH calculations use antilog (concentration = 10-pH). In acoustics, decibel conversions use antilog (power ratio = 10dB/10). In seismology, the Richter scale uses antilog (each whole number increase represents 10× more amplitude). In electronics, gain calculations frequently require antilog operations.
Antilog Reference Table (Base 10)
| y (log value) | antilog₁₀(y) = 10^y | Application |
|---|---|---|
| -3 | 0.001 | Milliunits, pH 3 = 0.001 M H⁺ |
| -2 | 0.01 | Centiunits, 1% = 0.01 |
| -1 | 0.1 | Deciunits, pH 1 = 0.1 M H⁺ |
| 0 | 1 | Unity, any base^0 = 1 |
| 1 | 10 | Decade, 10 dB = 10× power |
| 2 | 100 | Hectounits, 20 dB = 100× power |
| 3 | 1000 | Kilounits, Richter 3 = 1000 amplitude |
| 6 | 1000000 | Megaunits, 60 dB = 10⁶× power |
Frequently Asked Questions
What is antilog?
Antilog is the inverse function of the logarithm. If logb(x) = y, then antilogb(y) = x = by. It reverses the logarithm operation by raising the base to the given power.
How to calculate antilog base 10?
To calculate antilog base 10, raise 10 to the power of the given number. For example, antilog₁₀(3) = 10³ = 1000. On a calculator, use the 10^x button or type 10^y.
What is the difference between log and antilog?
Log finds the exponent: log₁₀(1000) = 3 (what power of 10 gives 1000?). Antilog finds the number: antilog₁₀(3) = 1000 (10 raised to power 3). They are inverse operations that undo each other.
What is natural antilog?
Natural antilog uses base e (≈ 2.71828). It is written as e^y or exp(y). For example, antilog_e(1) = e¹ = 2.71828. It is the inverse of the natural logarithm (ln).
Where is antilog used in real life?
Antilog is used in pH calculations (H⁺ concentration = 10^(-pH)), decibel conversions (power = 10^(dB/10)), Richter scale (amplitude = 10^magnitude), population growth models, and compound interest calculations.
Objective of Measurement:
Measurement is the most important aspect of our life. We use measurement in science, engineering, business trading, personal life, education, and more other fields. As technology is growing day by day so we need a highly accurate and easy convenient global measuring system in each and every field. It is essential to use standard measurement in every field that everyone to be sure that they not get cheated.
History of Measurement:
In history for measurement people used the human body as a tool. For measuring length used forearm, hand, foot & finger as a unit. The foot, finger is a subdivided shorter unit of a length. This type of measurement is not accurate cause different in size of the arm & finger for different people & some of the countries still using it. In history, there were lots of measuring systems developed but mostly used imperial, the metric system of measurement. We use these systems for measure distances, volume, weight, speed, area etc. Due to this a major problem everyone is facing while doing trading between the countries. A huge improvement in civilization, It necessary to improve measuring standards. Nowadays International Standard (SI) units are used as a global measurement system.