Math · Logarithms

Log Calculator

Compute the logarithm of any positive number in any base — base 2, 10, e (natural log) or a custom base — with instant verification.

Value x (> 0)

Base

log_b(x)

Natural log ln(x)

Common log log₁₀(x)

Binary log log₂(x)

Verification b^y

Change of base (ln x / ln b)

Definition: y = log_b(x) means b^y = x, for x > 0 and b > 0, b ≠ 1.
Change of base: log_b(x) = ln(x) / ln(b).
Special values: log_b(1) = 0, log_b(b) = 1, log_b(x·y) = log_b(x) + log_b(y).

Any base

Common log, natural log, binary log or a fully custom base.

Inverse verification

Every result is checked by raising the base to the returned power.

Multiple logs at once

See ln, log10 and log2 alongside the requested logarithm.

Handles fractions

Works for x < 1 and any positive real value.

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