What is Log?
A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log₁₀(100) = 2 because 10² = 100.
Logarithms are used in science (pH scale, Richter scale, decibels), finance (compound interest), and computer science (algorithm complexity).
Formula
log_b(x) = ln(x) / ln(b) log₁₀(x) = log(x) / log(10) ln(x) = natural logarithm (base e = 2.71828) log₂(x) = log(x) / log(2)
Rules: log(a×b) = log(a) + log(b) log(a/b) = log(a) − log(b) log(a^n) = n × log(a)
How to use this Log Calculator?
1. Enter the number. 2. Enter the base (default 10). 3. See log with your base, log₁₀, natural log, and log₂.