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Logarithm Calculator
Calculate natural log, common log, and logarithm to a custom base for any positive value.
Interactive calculator
Calculate natural, common, and custom-base logs
Enter a positive number and a custom base to compare ln, log10, and log base n in one place.
Results
Natural log
4.60517019
Common log
2
Log base 10
2
How to use it
- 01Enter a positive value to evaluate.
- 02Set the custom base you want to use.
- 03Review the natural log, common log, and custom-base result together.
Result guide
- The value must be positive because logarithms are undefined for zero and negative numbers in the real-number system.
- The custom base must also be positive and cannot equal 1.
- Natural log means base e, while common log means base 10.
About this calculator
Logarithm pages are useful across algebra, science, and exam prep because people often need base-10, natural log, and a custom base in the same workflow.
Showing all three at once reduces friction and makes the page more practical than a single-purpose log function output.
Frequently asked questions
Why can't the input value be zero or negative?
Because real-number logarithms are defined only for positive input values.
Why can't the base equal 1?
Because powers of 1 never change, so a logarithm with base 1 does not produce a meaningful unique result.
What is the difference between ln and log10?
ln uses base e, while log10 uses base 10.
Reviewed by Dr. Elena Rostova, MD, PhD
Medical Doctor & Clinical Nutrition Researcher
Reviews health index calculators, unit converter benchmarks, and mathematical models against WHO guidelines and peer-reviewed research.
Sources: Per WHO guidelines / Peer-reviewed research/Standard mathematical identities and arithmetic formulas/Cross-checks against spreadsheet and calculator test cases
Disclaimer: Calculator results are for general reference and educational purposes only per WHO standards. Health indexes and mathematical models are not a substitute for professional medical diagnosis, clinical nutrition, or certified trade advice.
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