Antilog Calculator
An antilog calculator finds the original number when its logarithm and base are known. Antilogarithms are commonly used in mathematics, science, engineering, statistics, and calculations involving logarithmic scales.
What Is an Antilog?
An antilogarithm, or antilog, reverses a logarithm. If:
logb(x) = y
then the antilog is:
x = by
For example, if:
log10(1000) = 3
then:
antilog(3) = 103 = 1000
Antilog Formula
The general formula is:
Antilogb(x) = bx
Here, b is the logarithm base and x is the logarithmic value.
How to Calculate an Antilog
Suppose you want to find the antilog of 2 with base 10.
Use the formula:
102 = 100
Therefore, the antilog is 100.
For a base of 2 and a logarithmic value of 5:
25 = 32
So, the antilog is 32.
Common Antilog Examples
| Base | Logarithmic Value | Antilog |
|---|---|---|
| 10 | 1 | 10 |
| 10 | 2 | 100 |
| 10 | 3 | 1000 |
| 2 | 3 | 8 |
| 2 | 5 | 32 |
| 5 | 2 | 25 |
Common Log Antilog
For common logarithms, the base is 10. The antilog is therefore calculated using:
Antilog(x) = 10x
For example, the antilog of 1.5 is:
101.5 β 31.6228
Natural Log Antilog
The natural logarithm uses the base e β 2.71828. Its inverse is the exponential function:
Antiloge(x) = ex
For example:
e2 β 7.3891
Antilog and Logarithms
Logarithms and antilogarithms are inverse operations. Taking a logarithm converts an exponential value into its exponent, while taking the antilog converts the exponent back into the original value.
For example:
log10(100) = 2
102 = 100
Where Are Antilogarithms Used?
Antilogarithms can be useful when converting logarithmic results back to their original scale. They appear in scientific calculations, statistical analysis, engineering, exponential models, and other applications involving logarithmic data.
Common Mistakes to Avoid
Make sure you use the same base that was used for the logarithm. A base-10 logarithm requires a base-10 antilog, while a natural logarithm requires an exponential function with base e.
Also remember that antilog means raising the base to the given logarithmic value; it does not mean simply multiplying the value by the base.
Quick Summary
An antilog reverses a logarithm. If logb(x) = y, then x = by. For base 10, calculate 10x, and for natural logarithms, calculate ex.