Logarithm Calculator

Calculate natural log (ln), log base 10, log base 2, or any custom base logarithm.

Frequently Asked Questions

What does log mean?

log_b(x) answers "what power do I raise b to in order to get x?" So log₁₀(1000) = 3 because 10³ = 1000. It is the inverse of exponentiation.

When do I use natural log (ln) vs log base 10?

Use ln in continuous growth, calculus, and most physics/biology. Use log₁₀ in pH, decibels, and the Richter scale. Computer science often uses log₂.

How do I change bases?

log_b(x) = log(x) / log(b) using any base. So log₂(32) = log(32)/log(2) = 5. This lets a calculator with only ln or log₁₀ compute any base.

Why can't I take the log of zero or a negative number?

No real exponent of a positive base produces 0 or a negative result. log(0) approaches negative infinity, and log of negatives gives complex numbers.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.