This log calculator finds the logarithm of any positive number in base 10, base e (natural log), base 2 or a custom base, and shows all three common logs at once.
What a logarithm means
log_b(x) = y means bʸ = x
A logarithm answers “what power do I raise the base to, to get this number?” For other bases the calculator uses the change-of-base rule: log_b(x) = ln(x) ÷ ln(b).
Worked example
log₁₀(1000) = 3, because 10³ = 1000. In the same way, log₂(1024) = 10 and ln(e²) = 2.
Frequently asked questions
Why can’t I take the log of zero or a negative number?
No power of a positive base gives zero or a negative number, so these logs are undefined in real numbers.
Where are logarithms used?
The pH scale, decibels and the Richter scale are all logarithmic, and logs are used to solve for time in growth and interest formulas.