A logarithm is the exponent to which a base must be raised to produce a given positive number.

ln is the natural logarithm with base e, approximately 2.71828.

log10 is the base-10 logarithm; for example, log10(1000) = 3.

How do I calculate a custom-base logarithm?

Use the change-of-base formula: log_b(x) = ln(x) / ln(b).

An antilog reverses a logarithm. For example, the base-10 antilog of 3 is 10³ = 1000.

Can I take the logarithm of a negative number?

Not in the real number system. This calculator accepts only positive logarithm arguments.

Can the logarithm base equal 1?

No. A valid real logarithm base must be positive and different from 1.

Tools/🧮 Calculators/Logarithm Calculator

Logarithm Calculator

Calculate natural logarithms, log10, custom-base logarithms, antilogs, and change-of-base results.

Version 1.0 · Last Updated: August 11, 2026 · Maintained by ToolLarder

Online logarithm, ln, log10, and antilog calculator

Find the natural logarithm, base-10 logarithm, or a logarithm in any valid custom base. The same calculator also handles antilogarithms and shows change-of-base calculations.

Natural logarithm (ln)

The natural logarithm uses e as its base and appears throughout science and mathematics.

ln(x) = logₑ(x)

Base-10 logarithm (log10)

The common logarithm tells you which power of 10 produces a number.

log₁₀(x) = y ⇔ 10ʸ = x

Custom-base logarithm

Choose base 2, 3, or any other valid base and calculate its logarithm directly.

log_b(x) = ln(x) / ln(b)

Antilog calculator

An antilog reverses a logarithm by raising the selected base to the entered exponent.

antilog_b(y) = bʸ

Logarithm change of base

Rewrite a logarithm in another computable base and inspect its numerator and denominator.

log_b(x) = log_k(x) / log_k(b)

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