Logarithm Calculator

Any base, via the change-of-base identity.

Any base, via the change-of-base identity. A logarithm answers the question: what power gives this number.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Value

Base

10 for common logs, 2.71828 for natural.

log₍10₎(1,000)

10^3 = 1,000

Log base 103

Natural log (ln)6.907755

Common log (log₁₀)3

Binary log (log₂)9.965784

Check: base^result1,000

Every logarithm is a rescaling of every other, so only one needs computing: log_b(x) = ln(x) ÷ ln(b). That change-of-base identity is why a calculator with just ln and log₁₀ can produce any base at all. A logarithm answers "what power gives this number" — here 10 raised to 3 returns 1,000.

How the Logarithm Calculator works

A logarithm answers the question: what power gives this number. Every logarithm is a rescaling of every other, so only one needs computing — log_b(x) = ln(x) ÷ ln(b). That identity is why a calculator with just ln and log₁₀ can produce any base at all.

Also known as: log calculator · natural log calculator · ln calculator · log base 2 calculator

Where to go next

The Logarithm question rarely arrives on its own. These are the ones that usually come with it:

Exponent Calculator — Powers, including negative and fractional exponents.
Exponential Growth Calculator — Growth or decay, with doubling time and half-life.
Square Root Calculator — Any root, with the simplified surd where one exists.
Percentage Calculator — Every common percentage question in one place.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

What is a logarithm?

The inverse of exponentiation. log₁₀(1000) = 3 because 10³ = 1000.

What is the difference between log and ln?

Base. 'log' usually means base 10 and 'ln' means base e, about 2.71828. Both are shown here alongside base 2.

What is the change-of-base formula?

log_b(x) = ln(x) ÷ ln(b). It lets any base be computed from natural logs alone, which is exactly what this page does.

Why can't I take the log of a negative number?

Because no real power of a positive base produces a negative result. The logarithm of a negative number exists only in complex numbers.

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The one-line version

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