Log Base N Calculator
Calculate a logarithm to any base, not just base 10 or natural log, using the change of base formula, free in your browser.
Enter Values
Minimum 0
Minimum 0
How to use this calculator
- Enter the value and the base.
- Read the logarithm.
How it works
log base b of x = ln(x) ÷ ln(b) — the change-of-base formula.
Worked example
log base 10 of 1000. = 3.
Common mistakes
- Using base 1 or a non-positive base/value — these are undefined.
- Confusing log base 10 with the natural log (base e).
Frequently asked questions
How do I calculate a logarithm in any base?
Use the change-of-base rule: log_n(x) = ln(x) ÷ ln(n). For example log base 2 of 8 = ln 8 ÷ ln 2 = 3.
What is a logarithm?
The power a base must be raised to in order to give a number: log base 10 of 1000 is 3 because 10³ = 1000.
What bases are common?
Base 10 (common log), base e (natural log, ln) and base 2 (used in computing). This tool handles any valid base.
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Cite this tool
Zerdly. (2026). Log Base N Calculator. Retrieved from https://www.zerdly.com/tools/log-base-n-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.