Calculate Antilog Instantly
Enter a logarithmic value and base to calculate the antilog, b^x, instantly. Use base 10 for common logs, e for natural logs, base 2 for binary logs, or any custom positive base.
What is an Antilog?
An antilog (or antilogarithm) is the inverse operation of a logarithm. If a logarithm asks "what power gives me this number?", an antilog asks "if the power is this, what is the number?"
Put simply: if log₁₀(x) = 3, then antilog₁₀(3) = 10³ = 1,000.
Antilog Quick Reference Table (Base 10)
The most commonly searched antilog values — all using the common log base of 10:
| x (log value) | Antilog₁₀(x) = 10ˣ |
|---|---|
| −2 | 0.01 |
| −1 | 0.1 |
| 0 | 1 |
| 0.5 | ≈ 3.162 |
| 1 | 10 |
| 1.5 | ≈ 31.62 |
| 2 | 100 |
| 2.5 | ≈ 316.2 |
| 3 | 1,000 |
| 4 | 10,000 |
Antilog of Common Values
- Antilog of 2 (base 10) → 10² = 100
- Antilog of 3 (base 10) → 10³ = 1,000
- Antilog of 0.5 (base 10) → 10⁰·⁵ ≈ 3.162
- Antilog of −1 (base 10) → 10⁻¹ = 0.1
- Natural antilog (antilog of 2, base e) → e² ≈ 7.389
How to Find Antilog on a Scientific Calculator
Most scientific calculators don't have a dedicated "antilog" button, but the function is always available:
For Base 10 (Common Antilog):
- Press 2nd or Shift key
- Press the log button (which activates 10ˣ)
- Enter your value and press =
For Natural Antilog (Base e):
- Press 2nd or Shift key
- Press the ln button (which activates eˣ)
- Enter your value and press =
Antilog Using an Antilog Table (Manual Method)
If you're using a printed antilog table (common in board exams that ban calculators):
- Separate your number into the characteristic (integer part) and mantissa (decimal part).
- Example: For 2.4567 → characteristic = 2, mantissa = .4567
- Look up the first two mantissa digits (.45) in the left column of the antilog table.
- Find the third mantissa digit (6) in the top row of the table.
- Apply mean difference for the fourth digit (7) from the right-hand column.
- Place the decimal and apply the characteristic: result × 10^characteristic.
The Relationship Between Logs and Antilogs
Logarithms and antilogarithms are inverse functions — like multiplication and division are inverses of each other.
- If log₁₀(1000) = 3, then antilog₁₀(3) = 1,000
- If ln(1) = 0, then antilog_e(0) = e⁰ = 1
- If log₂(8) = 3, then antilog₂(3) = 2³ = 8
Practical Application: pH to Concentration
In chemistry, pH = −log₁₀[H⁺]. If a solution has a pH of 4:
- log₁₀[H⁺] = −4
- [H⁺] = antilog₁₀(−4) = 10⁻⁴ = 0.0001 mol/L
This is the core reason antilog calculations appear so frequently in chemistry and biology coursework.