Logarithm & Exponential Calculator
Compute log base 10, natural log, any custom-base log, powers, roots, and exponential values in one place.
Disclaimer. This calculator is provided for educational and general-purpose use. Verify critical or high-stakes calculations independently before relying on them. Read full disclaimer →
About Logarithm and Exponential Calculator
Logarithms and exponentials are inverse operations. Log base b of x equals y means b raised to y equals x. Common logarithm uses base 10; natural logarithm ln(x) uses base e (approximately 2.71828). Key identities: log(a times b) = log(a) + log(b); log(a divided by b) = log(a) minus log(b); log(a to the n) = n times log(a).
The exponential growth model A = A0 times e to the rt is used for population growth, continuously compounded interest, radioactive decay, and epidemic modelling. Decibels in audio use log base 10. pH in chemistry = negative log of hydrogen ion concentration. The Richter earthquake scale uses log base 10. The natural log derivative equals 1 over x, making it fundamental in calculus and solving differential equations.
More Standalone Math & Statistics Calculators
Each tool below is also available as its own dedicated page with a full explanation, formula reference, and worked example: