Mathematics, Statistics & Geometry

Antilog Calculator

Calculate the antilogarithm for any base. Find 10^x, e^x, 2^x, or any custom base antilog with a clear step-by-step mathematical breakdown.

Antilog₍10₎(3)
1,000
10^x (Common Antilog)1,000
e^x (Natural Antilog)20.086
2^x (Binary Antilog)8
Calculation StepsCalculate antilog base 10 of 3 Antilog₍b₎(x) = b^x = 10^3 = 1000

Calculated locally in your browser. Fast, secure, and private.

Reverse the Logarithm

The Antilog calculator (or inverse logarithm calculator) allows you to find the original value when only the logarithm is known. This is a crucial step when converting logarithmic data—like pH values or decibel readings—back into their physical units of concentration or intensity.

antilogb(y)=by=x\begin{aligned} \text{antilog}_b(y) = b^y = x \end{aligned}

Where:
b=
The base of the original logarithm
y=
The value you are reversing the log for
x=
The original number before the log was taken

The Relationship Between Logs and Antilogs

Logarithms and antilogarithms are inverse functions, much like multiplication and division.

  • If log₁₀(100) = 2, then antilog₁₀(2) = 10² = 100.
  • If ln(1) = 0, then antilog_e(0) = e⁰ = 1.

How to Use This Calculator

  1. Enter the log value: This is the exponent or the 'result' of a previous log calculation.
  2. Select the base: Choose between common (10), natural (e), binary (2), or a custom base.
  3. Get the result: The tool calculates the base raised to the power of your input.

Practical Example: pH to Concentration

In chemistry, pH = -log₁₀[H+]. If you have a solution with a pH of 4:

  • -log₁₀[H+] = 4
  • log₁₀[H+] = -4
  • [H+] = antilog₁₀(-4) = 10⁻⁴ = 0.0001 mol/L

Scientific Accuracy

Our calculator provides high-precision results, essential for scientific calculations where small differences in logarithmic values lead to large differences in the antilog result.

Frequently Asked Questions

An antilogarithm is the inverse of a logarithm. It is the process of raising a base to a power to find the original number.

If you have a common log (base 10), the antilog of y is 10 raised to the power of y (10^y). For example, the antilog of 3 is 10³ = 1000.

The inverse of the natural logarithm (ln) is the exponential function e^x. The antilog of y (base e) is e^y.

While 'antilog' was common in the era of slide rules and log tables, today it is more commonly referred to simply as exponentiation or 'inverse log'.

No. If the base is positive (which it must be for standard logs), raising it to any power results in a positive number. However, the input 'y' can be negative.

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