Logarithm Calculator
The logarithm of any number, in base 10, base 2, e, or a base of your choosing.
What a logarithm answers
log_b(n) asks: to what power must b be raised to get n? log₁₀(1000) = 3 because 10³ = 1000. Any base can be computed from any other with the change-of-base formula, log_b(n) = ln(n) / ln(b), which is exactly what this calculator does.
Which base when
Base 10 for orders of magnitude (pH, decibels, earthquake scales), base 2 for anything counting doublings (algorithms, bits, compound growth doubling times), and base e wherever calculus is involved, because it is the one base whose exponential is its own derivative.