A logarithm calculator computes log_b(x), the logarithm of a value x with any base b.
About this calculator
A logarithm calculator computes log_b(x), the logarithm of a value x with any base b. The logarithm answers the question: 'b raised to what power gives x?' Logarithms are the inverse of exponentiation.
Logarithms appear in many real-world applications: decibels (sound), the Richter scale (earthquakes), pH (acidity), information theory (Shannon entropy), and many scientific and engineering formulas.
Common uses
- Calculate log base 10 for scientific notation and decibels
- Compute natural log (ln) for continuous growth and physics calculations
- Find logarithm base 2 for information theory and computer science
- Solve exponential equations using logarithms
Frequently asked questions
What is a logarithm?
A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log₁₀(1000) = 3 because 10³ = 1000. Common logarithm uses base 10 (log), natural logarithm uses base e ≈ 2.718 (ln).
What are logarithm rules?
Product rule: log(a × b) = log(a) + log(b). Quotient rule: log(a/b) = log(a) − log(b). Power rule: log(a^n) = n × log(a). Change of base: log_b(x) = log(x) / log(b). These rules allow simplification of complex logarithmic expressions.