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Logarithm Calculator

Calculates the logarithm of a number for any positive base.

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Result

log₍base₎(value)

3

Working

log₍2₎(8) = ln(8) / ln(2) = 3

Notes

  • · Uses the change-of-base formula: log_b(x) = ln(x) / ln(b). Value and base must be positive, and base ≠ 1.

Logarithm Calculator — How It Works

Logarithm Calculator — How It Works

A logarithm answers the question “what power do I need to raise the base to, to get this value?” The Logarithm Calculator works for any positive base (other than 1).

The formula (change of base)

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

Example

log₂(8) = ln(8) / ln(2) ≈ 2.0794 / 0.6931 = 3

(because 2³ = 8)

Tips

  • Both the value and the base must be positive numbers, and the base can’t be 1.
  • Common bases: base 10 (the “common log”), base e ≈ 2.71828 (the “natural log”), and base 2 (used heavily in computer science).

Try the Logarithm Calculator — instant results, no sign-up.

FAQ

Is this free?

Yes — the Logarithm Calculator runs entirely in your browser, no sign-up required.

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