Logarithm Calculator
Find the exponent needed to produce a positive argument in a chosen base.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Logarithm Calculator
A logarithm answers which exponent turns the base into the argument. Enter the argument and base as numbers; the base must be positive and different from one. The change-of-base identity lets the calculator use the browser’s natural logarithm implementation for arbitrary valid bases. A base between zero and one is allowed and can give a negative answer for an argument above one.
The calculation
Worked example
log base 10 of 1,000 is 3 because 10³ = 1,000. Log base 2 of 32 is 5 because 2⁵ = 32.
Assumptions and limits
Only real logarithms are supported, so zero and negative arguments are invalid. Bases very close to one can make results numerically sensitive because ln(base) is close to zero. The display rounds to ten decimal places, and no exact symbolic form is promised. To evaluate several operations together, use the Scientific Calculator.
Common questions
Why is base 1 invalid?
One raised to any power stays one, so it cannot provide a unique logarithm for general arguments.
What is a natural logarithm?
It uses the constant e as its base. The Scientific Calculator provides ln(x) directly.