Logarithm Calculator

Calculate common logarithms, natural logarithms, and logarithms with any base instantly. Free online logarithm calculator with formulas.

Frequently Asked Questions

What is the difference between log and ln?
Log (common logarithm) uses base 10, while ln (natural logarithm) uses base e (approximately 2.718). Natural logs are used in calculus and science, common logs in engineering.
Can I use any base for the logarithm?
Yes, the change of base feature lets you compute logarithms with any base using the formula log_b(x) = ln(x) / ln(b).
Can I calculate the logarithm of a negative number?
Logarithms of negative numbers are undefined in the real number system. This calculator works within the real number domain and requires positive inputs.
Verified 2026 formulas