Log Calculator

Calculate the logarithm of any number in any base — log₁₀, ln (base e), log₂, or a custom base you choose.

Logarithm Formulas

log_b(x) = ln(x) / ln(b)
TypeBaseExample
Common log10log(1000) = 3
Natural loge ≈ 2.71828ln(e²) = 2
Binary log2log₂(8) = 3

Key Properties

  • Product: log(A × B) = log(A) + log(B)
  • Quotient: log(A / B) = log(A) − log(B)
  • Power: log(Aⁿ) = n × log(A)
  • log_b(b) = 1 always
  • log_b(1) = 0 always

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