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Logarithm Calculator
Find the log of a number in any base, plus ln, log₁₀ and log₂.
Logarithm
—
log of the number.
| Natural log (ln) | — |
|---|---|
| Log base 10 | — |
| Log base 2 | — |
| Number | — |
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Enter your figures above to see the step-by-step working.
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How the Logarithm Calculator Works
A logarithm answers “what power do I raise the base to, to get this number?” The common log (base 10) of 1000 is 3, because 10³ = 1000. This calculator computes the log in any base — it converts using ln(x) ÷ ln(base) — and also shows the natural log (base e), common log (base 10) and binary log (base 2) together.
Logs turn multiplication into addition, which is why they underpin everything from decibels and pH to earthquake magnitudes and slide rules.
logb(x) = ln(x) ÷ ln(b)
Frequently Asked Questions
What is a logarithm?
The exponent a base must be raised to in order to produce a number. log₁₀(1000) = 3 because 10³ = 1000.
What is the natural log?
The logarithm to base e (about 2.718), written ln. It appears throughout math and science.
How do you find a log in any base?
Divide the natural log of the number by the natural log of the base: log_b(x) = ln(x) ÷ ln(b).
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