📉 Logarithm Calculator
Calculate log base 10, natural log (ln), log base 2, and any custom base logarithm.
logb(x) = ?
log₁₀(x)
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log₁₀ (common)
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ln (natural)
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log₂ (binary)
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Antilog (10^result)
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Logarithm Formulas
logₐ(x) = log(x) / log(a) (change of base)
log(a × b) = log(a) + log(b) (product rule)
log(a / b) = log(a) − log(b) (quotient rule)
log(aⁿ) = n × log(a) (power rule)
log(a × b) = log(a) + log(b) (product rule)
log(a / b) = log(a) − log(b) (quotient rule)
log(aⁿ) = n × log(a) (power rule)
Applications
- Decibels (dB): Sound level = 10 × log₁₀(I/I₀)
- pH: pH = −log₁₀[H⁺]
- Richter scale: Each whole number = 10× more amplitude
- Information theory: log₂ measures information in bits