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Log Calculator (Logarithm)

The log calculator (logarithm) calculates the value of a logarithm with an arbitrary base.

Use 10 for common log, 2.718281828 for natural log.
Clear
log base 10310^3 = 1,000
log₁₀ (common)3
ln (natural)6.907755279
log₂ (binary)9.9657842847
Antilog check1,000

Change of base

log_b(x)ln(x) ÷ ln(b) = 6.907755 ÷ 2.302585 = 3
Alsolog₁₀(x) ÷ log₁₀(b) gives the same

The rule

log_b(x) = y means b^y = x

Logarithms turn multiplication into addition

The defining rules:

  • log(ab) = log a + log b
  • log(a/b) = log a − log b
  • log(aⁿ) = n · log a
  • log_b(x) = ln x ÷ ln b — change of base

That first rule is why logarithms were invented: before calculators, they turned long multiplications into lookups and additions.