Logarithm Calculator

Calculate logarithms with any base, including natural log (ln), common log (log₁₀), and binary log (log₂).

Logarithm Calculator

Quick Examples

How to Use

Enter Number
Input a positive number
Choose Base
Select common bases or enter custom
Get Result
See logarithm with detailed steps

Common Logarithms

log_10(1)
= 0
log_10(10)
= 1
log_10(100)
= 2
log_10(1000)
= 3
log_2(1)
= 0
log_2(2)
= 1
log_2(4)
= 2
log_2(8)
= 3

About Logarithm Calculator

A logarithm calculator finds the exponent to which a base must be raised to produce a given number.

Types of Logarithms

Common Logarithm (log₁₀)

Base 10 logarithm, widely used in science and engineering

Natural Logarithm (ln)

Base e logarithm (e ≈ 2.718), used in calculus and physics

Binary Logarithm (log₂)

Base 2 logarithm, important in computer science and information theory

General Logarithm

Logarithm with any positive base (except 1)

Logarithm Properties

  • • log_b(1) = 0 (for any base b)
  • • log_b(b) = 1 (for any base b)
  • • log_b(xy) = log_b(x) + log_b(y) (Product Rule)
  • • log_b(x/y) = log_b(x) - log_b(y) (Quotient Rule)
  • • log_b(x^n) = n × log_b(x) (Power Rule)
  • • log_b(x) = ln(x) / ln(b) (Change of Base Formula)