What is the natural logarithm?

The natural log (ln) uses base e ≈ 2.71828. It appears naturally in calculus, population growth, radioactive decay, and compound interest. ln(e) = 1.

Log base 2 (binary log) answers how many times 2 must be multiplied to get the number. Used in computer science — log₂(1024) = 10, meaning 1024 = 2¹⁰.

Can I calculate log of any base?

Yes, using the change of base formula: log_b(x) = ln(x) / ln(b). Our calculator uses this formula internally to compute any base.

Logarithm Calculator — Log, Ln, Log Base N

The Logarithm Calculator computes logarithms in any base — common log (base 10), natural log (base e), binary log (base 2), or any custom base you specify. Logarithms are the inverse of exponentiation and are used in science, engineering, acoustics (decibels), pH chemistry, information theory, and finance.

Number (x)

Log Base

Frequently Asked Questions

A logarithm answers: 'To what power must the base be raised to get this number?' log₁₀(100) = 2 because 10² = 100. Logarithm is the inverse of exponentiation.

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