# Antilog Calculator

Calculate the antilogarithm for base 10, base e, or any custom base. Also computes logarithms. antilog_b(x) = b^x.

## What this calculates

Find the antilogarithm (inverse log) for any base. The antilog of x in base b is simply b raised to the power x. For example, antilog base 10 of 3 is 10^3 = 1,000. You can also switch to log mode to find the exponent instead.

## Inputs

- **Mode** — options: Antilog (find the number), Log (find the exponent) — Antilog computes b^x. Log finds the exponent.
- **Base** — options: Base 10 (common), Base e (natural), Custom base — The base of the logarithm.
- **Custom Base Value** — Only used when 'Custom base' is selected above.
- **Value** — For antilog mode: the exponent x (find b^x). For log mode: the number (find log_b of it).

## Outputs

- **Result** — The computed antilog or log value.
- **Expression** — formatted as text — The mathematical expression evaluated.
- **Base Used** — formatted as text — The logarithmic base.
- **Inverse Operation** — formatted as text — The inverse result. If you computed antilog, this shows the log, and vice versa.

## Details

**What Is an Antilogarithm?**

The antilogarithm is the inverse of the logarithm. If log_b(y) = x, then antilog_b(x) = y. In plain terms:

**antilog_b(x) = b^x**

**Common Bases**

- **Base 10 (common log):** Used in scientific notation, decibels, and the Richter scale. antilog_10(2) = 100.
- **Base e (natural log):** Used in calculus, continuous growth/decay, and physics. antilog_e(1) = e = 2.71828.
- **Base 2:** Used in computer science. antilog_2(8) = 256.

**Worked Examples**

- antilog_10(4) = 10^4 = 10,000
- antilog_e(2) = e^2 = 7.389
- antilog_2(10) = 2^10 = 1,024

**The Log-Antilog Relationship**

Logarithm and antilogarithm are inverse operations:
- log_10(1000) = 3, and antilog_10(3) = 1000
- ln(7.389) = 2, and e^2 = 7.389

This calculator shows both directions, so you can verify one from the other.

## Frequently Asked Questions

**Q: What is an antilogarithm?**

A: An antilogarithm reverses a logarithm. If log base b of y equals x, then the antilog base b of x equals y. Practically, antilog_b(x) = b^x. For example, the common antilog of 2 is 10^2 = 100.

**Q: What is the difference between antilog and exponentiation?**

A: They are the same operation. The antilogarithm base b of x is just b raised to the power x. The term 'antilog' is used specifically in the context of logarithms to emphasize that it is the inverse operation of taking a log.

**Q: How do you calculate antilog on a regular calculator?**

A: For common antilog (base 10), use the 10^x button. For natural antilog (base e), use the e^x button. For other bases, compute b^x using the exponentiation key (usually y^x or ^). On a phone, the scientific mode typically has these buttons.

**Q: Can the antilog be negative?**

A: The antilog of any real number (for positive base) is always positive, since b^x > 0 for any positive base b and any real exponent x. However, the input to the antilog (the exponent) can be negative: antilog_10(-2) = 10^(-2) = 0.01.

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Source: https://vastcalc.com/calculators/math/antilog
Category: Math
Last updated: 2026-04-08