inverse log calculator

What is an inverse log?

An inverse logarithm (also called an antilog) reverses a logarithm. If a logarithm tells you the exponent, the inverse log gives you the original number. In plain terms: logarithms compress large and small values, while inverse logs restore them.

Core formula

If you have:

logb(x) = y

then the inverse operation is:

x = by

• b is the base (10, e, 2, or custom)
• y is the log value
• x is the recovered original value

Common inverse log cases

1) Common log (base 10)

log(x) = y means x = 10y.

2) Natural log (base e)

ln(x) = y means x = ey.

3) Binary log (base 2)

log2(x) = y means x = 2y.

How to use this calculator

1. Enter your logarithm value y.
2. Select the base type (10, e, 2, or custom).
3. If using custom, enter the base and make sure it is valid (b > 0 and b ≠ 1).
4. Click Calculate to get the antilog result.

Quick examples

• If log(x) = 3, then x = 103 = 1000.
• If ln(x) = 2, then x = e2 ≈ 7.389.
• If log2(x) = -1, then x = 2-1 = 0.5.

Where inverse logs are used

Inverse logarithms show up in many practical fields:

• Finance: undoing continuous growth models.
• Science: converting pH and decibel scales back to linear values.
• Data analysis: reversing log-transformed variables for interpretation.
• Engineering: signal and control calculations involving exponential behavior.

Important input rules

• The base must be positive.
• The base cannot equal 1.
• Very large positive exponents can overflow in any calculator due to numeric limits.