Logarithm Calculator
Logarithm Calculator
Logarithms are the inverse of exponentiation. If bˣ = y, then log_b(y) = x. They are essential in science, engineering, and computer science.
Conversion Formula
log_b(x) = ln(x) / ln(b). This change-of-base formula lets us compute any logarithm using the natural logarithm function.
Step-by-Step Examples
value=100, base=10 = 2
10² = 100, so log₁₀(100) = 2
value=256, base=2 = 8
2⁸ = 256, so log₂(256) = 8
Frequently Asked Questions
What is a logarithm?
A logarithm answers: "To what power must the base be raised to get this value?" log₁₀(100) = 2 because 10² = 100.
What is the difference between log and ln?
log usually means base-10 (common log). ln means base-e (natural log), where e ≈ 2.71828. In math contexts, log sometimes means ln.
What is log base 2 used for?
Log base 2 is fundamental in computer science for measuring bits of information, algorithm complexity, and binary tree depths.
Can you take the log of zero or a negative number?
No. Logarithms are only defined for positive numbers. log(0) and log(-5) are undefined in real numbers.
What are the laws of logarithms?
log(a×b) = log(a)+log(b), log(a/b) = log(a)-log(b), log(aⁿ) = n×log(a). These make complex calculations simpler.