Calculate the logarithm of a number with any base. Enter the number and the base to find the answer instantly.
A logarithm answers the question: "what exponent must the base be raised to, to give this number?". The calculator uses the change-of-base formula to calculate logarithms with any base:
For example, log₁₀(100) = 2, because 10² = 100. The check field recalculates baseresult, which should give back the original number.
The natural logarithm is the logarithm with base e (Euler's number, about 2.71828). It's widely used in mathematics, physics and economics, including continuous growth and decay. Enter 2.71828 as the base to calculate ln.
Because no real exponent can turn a positive base into a negative number (a positive number raised to any real exponent is always positive). The logarithm of zero or negative numbers is therefore undefined among the real numbers.
Logarithms are used to measure sound level (decibels), earthquake strength (the Richter scale), pH in chemistry, and to analyze exponential growth and decay in economics and natural science.