Logarithm Calculator
Enter a number and choose the base to get its logarithm.
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What a logarithm is
The logarithm answers the question "to what power must the base be raised to get this number?" log₁₀(1000) = 3 because 10³ = 1000, and log₂(8) = 3 because 2³ = 8. The natural logarithm ln uses e ≈ 2.71828 as its base.
Rules
- log(a × b) = log a + log b, and log(a ÷ b) = log a − log b
- log(aⁿ) = n × log a
- Change of base: log_b(x) = ln(x) ÷ ln(b), which is how this calculator works for any base
Where logarithms appear
pH in chemistry, decibels for sound, the Richter scale for earthquakes, compound interest and population growth (time to double = ln 2 ÷ rate), and computer science (log₂ of n is how many times you can halve n). The antilog reverses a logarithm: the antilog of 3 in base 10 is 1000.
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How it works
- Enter — type or paste your values or text.
- Get the result — it is worked out in your browser.
- Adjust — change the inputs to compare, or copy the result.
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