Logarithm Calculator

Calculate natural logarithms (ln), common logarithms (log₁₀), and logarithms with any base

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Calculation Details

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log(xy) = log(x) + log(y)

log(x/y) = log(x) - log(y)

log(x^n) = n × log(x)

log_b(x) = ln(x) / ln(b)

log_b(b^x) = x

b^(log_b(x)) = x

ln(e) = 1, log₁₀(10) = 1

ln(1) = 0

ln(e) ≈ 1

ln(10) ≈ 2.303

log₁₀(1) = 0

log₁₀(10) = 1

log₁₀(100) = 2

log₁₀(1000) = 3

log₂(8) = 3

A logarithm is the inverse of exponentiation. If b^y = x, then log_b(x) = y. It answers: "To what power must we raise b to get x?"

The natural logarithm uses base e (≈2.718). It's widely used in calculus, physics, and engineering for exponential growth and decay.

Uses base 10 and is common in science and engineering. Useful for orders of magnitude and scientific notation.

Used in pH calculations, earthquake measurements (Richter scale), sound levels (decibels), and computer science algorithms.

Calculate powers and exponents

Advanced mathematical calculations

Calculate square roots and nth roots