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Logarithm Calculator

Calculate log₁₀, natural log (ln), log₂, or any custom base logarithm. Also computes the antilog (inverse logarithm).

Value (x)1000
x
Base
log₁₀(x)
ln(x) — natural log
log₂(x)
Antilog (10^result)
e^result
Frequently Asked Questions
What is a logarithm?

The inverse of exponentiation. log₁₀(1000) = 3 because 10³ = 1000. Answers "what power gives this number?"

What is the natural logarithm?

Uses base e ≈ 2.718. Appears in calculus, compound interest, and growth models. ln(e) = 1.

Difference between log and ln?

log uses base 10. ln uses base e. ln(x) = log(x) / log(e) ≈ log(x) / 0.4343.

What is log₂ used for?

Computer science. Gives number of bits needed to represent n values and steps in binary search.

How does log relate to decibels?

dB = 10 × log₁₀(intensity ratio). Sound 10 times more intense is 10 dB louder.