OceanCalc

Logarithm Calculator

Calculate logarithms with any base: natural log, common log, and custom bases.

Enter Values

Must be positive

Common bases: e (≈2.718), 10, 2

Logarithm Properties

Definition:

log_b(x) = y ⟺ b^y = x

Change of Base:

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

Common Types:

  • ln(x) = log_e(x) - Natural log
  • log(x) = log_10(x) - Common log
  • lg(x) = log_2(x) - Binary log

Properties:

  • log(a × b) = log(a) + log(b)
  • log(a / b) = log(a) - log(b)
  • log(a^n) = n × log(a)

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Logarithm Results
Log base 10 of 100
log₍10₎(100)2
ln(100) - Natural log4.6052
log₁₀(100) - Common log2
log₂(100) - Binary log6.6439
10^100 - Antilog1e+100