Logarithm calculator
Logarithms to any base, plus log₁₀, ln and log₂, and the inverse powers.
- log_b(x)
- 3
- log₁₀(x), common logarithm
- 3
- ln(x), natural logarithm
- 6.90776
- log₂(x), binary logarithm (octaves, bits)
- 9.96578
Back again: powers
- b^y (antilogarithm)
- 1000
- e^y
- 20.0855
Decibels use log₁₀, octaves and bits use log₂. Logarithms are only defined for positive numbers; the base must be positive and not 1.
How it works
The logarithm answers 'to which power must the base be raised?'. Decibels are built on log₁₀, octaves and bits on log₂.
Formulas
- log_b(x) = ln(x) / ln(b)
- x = b^y
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