Logarithm Calculator
Logarithm to a chosen base, plus natural and base-10 logs.
How it works
log_b(x) = ln(x) ÷ ln(b)
A logarithm is the inverse of exponentiation: log₁₀(100) = 2 because 10² = 100. x must be > 0.
Worked example
log₂(8) = 3 because 2³ = 8.
log₁₀(1000) = 3; ln(e²) = 2. If log₃(x) = 4, then x = 3⁴ = 81.
Notes and limitations
Logarithms are defined only for positive arguments, with a base greater than 0 and not equal to 1. Use the change-of-base formula logₐb = ln b ÷ ln a. Doubling time, decibels and earthquake magnitude are all logarithmic scales.