Logarithm Calculator

Find log base b of x, the power you raise b to in order to get x.

Type e for the natural log. Common bases: 10, 2, e.
Fractions and decimals both work.
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Logarithm
Natural log (ln x)
Common log (log₁₀ x)
Binary log (log₂ x)
Work

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How Logarithms Work

A logarithm answers "what power?": log_b(x) = y means bʸ = x. Any base can be found from natural logs with the change-of-base rule.

log_b(x) = ln(x) ÷ ln(b)
log(xy) = log x + log y   log(x/y) = log x − log y   log(xⁿ) = n log x

Worked Example

Tips

Only positive numbers have real logarithms, and the base must be positive and not 1. ln uses e ≈ 2.718281828.