Logarithm Calculator
Find a real logarithm for any positive number and valid positive base, alongside natural and base-10 logs.
What would you like to do next?
Evaluate a logarithm without changing bases by hand
Enter a positive number and a positive base other than one. The calculator uses the change-of-base relationship to display the requested logarithm, then shows natural and base-10 logarithms of the same number. The three results make it easier to check homework, growth models, information formulas and scientific calculations that use different conventional bases.
Keep the real-number domain visible
A real logarithm is defined here only for a positive input and a positive base that is not one. The page does not calculate complex logarithms, symbolic simplification or uncertainty from measured data. Preserve enough precision for the surrounding problem and verify whether a formula expects natural log, common log or another base before substituting the result.
Frequently asked questions
Can the base equal one?
No. A base of one cannot produce the required one-to-one exponential relationship.
What is natural logarithm?
It is the logarithm with base e and is shown as a separate result.
Are negative-number logarithms supported?
No. This tool is limited to real logarithms of positive numbers.