Logarithm Calculator
Calculate logarithms with any base, plus natural log (ln) and log base 2.
The Logarithm Calculator computes the logarithm of any positive number with any positive base. It also shows the natural logarithm (base e) and binary logarithm (base 2) simultaneously.
What is a Logarithm?
The logarithm log_b(x) answers the question: "To what power must b be raised to get x?" For example, log₁₀(100) = 2 because 10² = 100. Similarly, log₂(8) = 3 because 2³ = 8.
Common Logarithm Types
- Common log (base 10): Used in science, engineering, and decibel scales
- Natural log (base e ≈ 2.718): Used in calculus, growth/decay models, and statistics
- Binary log (base 2): Used in computer science, information theory, and algorithms
The calculator uses the change-of-base formula internally: log_b(x) = ln(x) / ln(b), which allows computing logarithms of any base from the natural logarithm.
Frequently Asked Questions
What is the difference between log, ln, and log₂?
log typically means base 10 (common logarithm), ln means base e ≈ 2.718 (natural logarithm), and log₂ means base 2 (binary logarithm). All are related by the change-of-base formula.
Can I take the logarithm of a negative number?
Not with real numbers. The logarithm is only defined for positive numbers. The logarithm of negative numbers requires complex analysis and is beyond this calculator.
What base should I use?
Use base 10 for general-purpose calculations, base e for calculus and growth models, and base 2 for computer science. Any other positive base is also valid.