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Scientific · Logarithm

Logarithm Calculator

Compute logarithms in any base.

Logarithm Calculator

Enter a positive value and a base (use "e" for the natural logarithm), then select Calculate.

How this is calculated

A logarithm answers "to what power must the base be raised to get this value?" Computed via the change-of-base identity: log_b(x) = ln(x) ⁄ ln(b)

Examples

log₁₀(100) = 2, since 10² = 100. log₂(8) = 3, since 2³ = 8. ln(e³) = 3, since the natural logarithm (base e) is the inverse of eˣ.

About this calculation

This uses the standard change-of-base logarithm identity, valid for any positive base other than 1, and any positive value.

Related tools

More calculators are on the way — browse everything planned on the Home page.

Frequently asked questions

What does "e" mean in the base field?

It stands for Euler's number (≈2.71828), giving the natural logarithm (usually written ln). You can also enter any positive number, like 10 (the common logarithm) or 2 (the binary logarithm).

Why does the calculator say my input is invalid?

The value must be a positive number (logarithms of zero or negative numbers aren't defined), and the base must be a positive number other than 1.