Antilogarithm Table (Base 10)
This antilogarithm table (base 10) helps you quickly find the number whose logarithm is a given value. In other words, it lets you look up the antilog of a log value. These tables were widely used before calculators and are still helpful for checking calculations in math, physics, engineering, and statistics.
What Is an Antilogarithm (Antilog)?
If you know that the base-10 logarithm of a number is y, then the original number is called the antilogarithm (or simply antilog) of y. In symbols:
If log10(x) = y, then x = 10y.
So the antilog of y (in base 10) is 10y.
How to Use This Antilogarithm Table
- Locate the logarithm value (log base 10) in the first column.
- Read the corresponding value in the second column. This is the antilog, i.e., the original number.
- Use the table for quick estimates and to verify calculator results.
The table below includes common base-10 logarithm values and their corresponding antilogarithms. In a traditional printed antilog table, you would typically find far more values (for example, logs with two or three decimal places). You can extend this table with more rows if you need a finer resolution.
Base-10 Antilogarithm Table
| log10(x) | x = antilog (10log) |
|---|---|
| -3 | 0.0010 |
| -2 | 0.0100 |
| -1 | 0.1000 |
| 0 | 1.0000 |
| 0.1 | 1.2589 |
| 0.2 | 1.5849 |
| 0.3 | 1.9953 |
| 0.4 | 2.5119 |
| 0.5 | 3.1623 |
| 0.6 | 3.9811 |
| 0.7 | 5.0119 |
| 0.8 | 6.3096 |
| 0.9 | 7.9433 |
| 1 | 10.0000 |
| 2 | 100.0000 |
| 3 | 1,000.0000 |
| 4 | 10,000.0000 |
Note: Values are rounded to four decimal places where appropriate.
Common Uses of Antilogarithms
Antilogarithms appear in many areas of science and engineering, such as:
- Reconstructing original values after using logarithms to simplify calculations
- Working with logarithmic scales (for example, pH, Richter, or decibel scales)
- Solving exponential and growth/decay equations
- Checking results from logarithm tables or calculators
Antilog vs. Logarithm
The logarithm of a number tells you the power to which the base must be raised to obtain that number. The antilog does the opposite: it takes the logarithm value and returns the original number.
- Logarithm (base 10):
log10(x) - Antilogarithm (base 10):
10ywherey = log10(x)
In simple terms: the antilog “undoes” the logarithm.
Frequently Asked Questions
Is this antilogarithm table for base 10 only?
Yes. This page shows an antilogarithm table for the common logarithm, which uses base 10. For natural logarithms (base e), you would use ey instead of 10y.
What is the difference between “antilog” and “antilogarithm”?
They mean the same thing. “Antilog” is just a shorter, more informal way of saying “antilogarithm”.
Can I extend this antilog table?
Yes. Traditional printed tables often include many more rows, usually with logarithm values from, for example, 0.00 to 0.99 with several decimal places. You can generate additional values using the formula x = 10y and add them as new rows to this table.
Is antilog the inverse of log?
Exactly. The antilog function is the inverse of the logarithm function. Applying log and then antilog (or the other way around) brings you back to your original number, as long as you use the same base.
Related Math Tables
If you are working with logarithms and antilogs, you may also find these tables useful: