㏒ Logarithm Calculator

Logarithm Result

What is a Logarithm?

A logarithm answers the question: "To what exponent must we raise the base to get this number?" If b^y = x, then log_b(x) = y.

log₁₀(100) = 2 (because 10² = 100)
ln(e) = 1 (because e¹ = e)
log₂(8) = 3 (because 2³ = 8)

Types of Logarithms

  • Common Log (log₁₀): Base 10, widely used in science and engineering.
  • Natural Log (ln): Base e (≈ 2.71828), used in calculus and natural growth models.
  • Binary Log (log₂): Base 2, used in computer science and information theory.

Frequently Asked Questions

What is log(1000)?
log₁₀(1000) = 3, because 10³ = 1000.
What is the natural log of e?
ln(e) = 1, because e¹ = e. Also, ln(1) = 0 and ln(e²) = 2.
What is log(0) or log of a negative number?
Logarithms of 0 or negative numbers are undefined in the real number system. You can only take the log of positive numbers.