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Logarithm (Any Base) Calculator
Compute the logarithm of a number in any base, plus its natural and base-10 logs.
Number
Base
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How it works
log_b(x) = ln(x) ÷ ln(b)
A logarithm answers "what power turns the base into this number?". Any base can be computed from natural logs using the change-of-base formula shown.
Worked example
log base 10 of 1000 = 3, because 10³ = 1000.
Frequently asked questions
Why must the base not be 1?
Base 1 raised to any power is always 1, so it cannot produce other numbers — the log is undefined.
What is ln?
The natural log uses base e ≈ 2.718, common in growth, decay and calculus.
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This calculator is for educational purposes. Double-check important results before acting on them.