help-calc

08 Numbers and Units

How to Find the Antilog (Inverse Log) of a Number

Card 08-0036 · Updated · Standard formula, shown below

Antilog (b to the power x) 316.2278
Natural antilog (e to the power x)
12.1825
Result, rounded to 4 decimal places
Logarithm value x
2.5
Input
Base
10
Input
You enter
Logarithm value x, Base
You get
Antilog (b to the power x), Natural antilog (e to the power x)
Rounding
4 dp

This calculator finds the antilogarithm of a number, the value whose logarithm it is. Enter the number and the base (10 for common logs); you get the antilog in that base and the natural antilog eˣ.

Formula

antilog_b(x) = bˣ, because log_b(bˣ) = x. The natural antilog is eˣ, with e ≈ 2.71828.

Worked Example

The antilog of 2.5 in base 10.

  1. 10^2.5 = 10² × 10^0.5 = 100 × 3.16228 = 316.2278
  2. e^2.5 = 12.1825

How to read the result

On a handheld calculator the antilog key is usually 10ˣ (often shift + log); for natural logs use eˣ (shift + ln). Check: log₁₀ 316.2278 = 2.5.

Limits and common mistakes

  • The base must be positive and not 1.
  • Very large x overflows; the calculator limits x to ±300.

Frequently Asked Questions

What is the antilog of 2?

100 in base 10.

What is the antilog of −1?

0.1 in base 10.

How do I find antilog on a calculator?

Press shift (or 2nd) and log to get 10ˣ, then type the number.

Is antilog the same as exponent?

Yes: antilog_b(x) = bˣ.

Formula used
in x | Logarithm value x | - | 2.5 | -300 | 300
in b | Base | - | 10 | 0.000001 | 1000000
out y | Antilog (b to the power x) | - | b^x | 4
out ex | Natural antilog (e to the power x) | - | exp(x) | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.