Logarithm Calculator

Calculate logarithms with any base. Supports common log (base 10), natural log (base e), binary log (base 2), and custom bases.

Calculate Logarithm
Select the logarithm type and enter a number
Result

Enter a number to calculate its logarithm

Logarithm Reference

Common Log (log₁₀)

log₁₀(1) = 0
log₁₀(10) = 1
log₁₀(100) = 2
log₁₀(1000) = 3

Natural Log (ln)

ln(1) = 0
ln(e) ≈ 1
ln(10) ≈ 2.303
e ≈ 2.71828

Binary Log (log₂)

log₂(1) = 0
log₂(2) = 1
log₂(8) = 3
log₂(1024) = 10
Frequently Asked Questions

What is a logarithm?

A logarithm answers: what power must we raise the base to get a number? For example, log₁₀(100) = 2 because 10² = 100.

What is the natural logarithm?

The natural logarithm (ln) uses Eulers number e (≈ 2.71828) as its base. It appears frequently in calculus and physics.

How do I convert between logarithm bases?

Use the change of base formula: logₐ(x) = ln(x) / ln(a) = log₁₀(x) / log₁₀(a).

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