justyourcalculatorLog Calculator (Logarithm)
Work out logarithms in any base, or solve for the number or the base.
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Log Calculator
Logarithms in any base, solve for any value
Type e for the natural log.
log₍10₎ 1,000
3
- ln x (base e)
- 6.907755278982
- log₁₀ x
- 3
- log₂ x
- 9.965784284662
How it was calculated
- log_10(1,000) = ln(1,000) / ln(10) (change of base)
- = 6.907755278982 / 2.302585092994
- = 3
- Check: 10^3 = 1,000
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How the log calculator works
A logarithm answers the question "what power do I raise the base to, to get this number?" log_b(x) = y means b^y = x. So log₁₀(1000) = 3 because 10³ = 1000.
Calculators usually only have ln (base e ≈ 2.71828) and log (base 10), so other bases use the change-of-base rule: log_b(x) = ln(x) / ln(b). This calculator applies it for any base and shows the check b^y = x.
Logs are only defined for positive numbers, and the base must be positive and not equal to 1.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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