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Logarithm Calculator
Calculate natural log, common log, and logarithm to a custom base for any positive value.
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Algebra and science utility
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.
Why this page matters
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.
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