Logarithm Calculator
Calculate the logarithm of a number to any base, including common log (base 10) and natural log (base e).
Your results
Calculation breakdown
- Logarithm
- log_base(x) = ln(x) ÷ ln(base)
Worked example
log base 10 of 100 is 2, since 10 squared equals 100.
Assumptions
- Logarithms of zero or negative numbers are undefined and return an error.
- The base must be a positive number other than 1.
How this calculator works
This calculator finds the logarithm of a positive number to a base you choose, including base 10 and base e (natural log). It uses the change-of-base formula to support any positive base other than 1.
Frequently asked questions
What is a logarithm?
A logarithm answers the question: to what power must the base be raised to produce this number? For example, log base 10 of 100 is 2, since 10 squared is 100.
Can I find a logarithm of a negative number?
No, logarithms of zero or negative numbers aren't defined for real numbers, so the calculator shows an error.
What is natural log used for?
Natural log (base e) commonly appears in continuous growth and decay problems, such as compound interest calculated continuously.