Logarithm Calculator
Calculate logarithms with any base. Computes log base b of x along with natural log (ln) and common log (log₁₀).
Enter a number and base to calculate the logarithm.
Logarithm Formula
logb(x) = y means by = x
Change of base: logb(x) = ln(x) / ln(b)
Change of base: logb(x) = ln(x) / ln(b)
A logarithm answers the question: "To what power must I raise the base to get x?"
Common Logarithm Types
- Common log (log₁₀): Base 10, used in science and engineering.
- Natural log (ln): Base e ≈ 2.71828, used in calculus and natural sciences.
- Binary log (log₂): Base 2, used in computer science.
Examples:
log₁₀(100) = 2 (because 10² = 100)
ln(e) = 1 (because e¹ = e)
log₂(8) = 3 (because 2³ = 8)
log₁₀(100) = 2 (because 10² = 100)
ln(e) = 1 (because e¹ = e)
log₂(8) = 3 (because 2³ = 8)
Logarithm Properties
- logb(xy) = logb(x) + logb(y)
- logb(x/y) = logb(x) − logb(y)
- logb(xn) = n × logb(x)
- logb(1) = 0
- logb(b) = 1
Related Calculators
Last updated: 2026-08-08