Logarithm Calculator
Calculate the logarithm of a number in any base. Common defaults: ln (base e), log₁₀ (base 10), log₂ (base 2 for computing).
Inputs
Common: 10 (log), e ≈ 2.71828 (ln), 2 (binary).
Logarithm
—
Natural log (base e)
—
Common log (base 10)
—
Binary log (base 2)
—
Check: base^result
—
About Logarithm Calculator
What is a logarithm?
logₐ(x) is the exponent you need to raise a to in order to get x. log₁₀(100) = 2 because 10² = 100. They’re the inverse of exponentiation.
Common bases
Base 10 (called log): everyday math, decibels, pH. Base e ≈ 2.718 (called ln, natural log): calculus, continuous growth. Base 2 (log₂): computer science, information theory.
Change of base
logₐ(x) = ln(x) / ln(a) = log(x) / log(a). This calculator uses that formula to handle any base from the natural log built into JavaScript.