What is the Logarithm Calculator?
Calculate logarithms online for free with this logarithm calculator. Compute natural log (ln), common log (log₁₀), binary log (log₂), custom-base logs, and antilogs (bʸ). Each result includes change-of-base steps, formula notation, and verification that base^answer equals your input. Runs entirely in your browser with no signup.
How to use the Logarithm Calculator
- Choose a mode: natural, common, binary, custom base, or antilog.
- Enter the value (or exponent for antilog) and base if needed.
- Click Calculate.
- Review the result, formula, and verification.
- Copy the numeric result or the full summary with steps.
Common use cases
- Computing ln(e) = 1 for calculus homework
- Finding log₁₀(1000) = 3 for pH or decibel scales
- Calculating 2¹⁰ = 1024 with the antilog mode
Frequently asked questions
- What is a logarithm?
- A logarithm answers: to what exponent must the base be raised to get a given number? For example, log₁₀(1000) = 3 because 10³ = 1000.
- What is the difference between ln and log?
- ln(x) is the natural logarithm with base e ≈ 2.71828. log₁₀(x) is the common logarithm with base 10. In this tool, log₁₀ is labeled Common (log₁₀).
- How does change of base work?
- log_b(x) = ln(x) ÷ ln(b), or equivalently log₁₀(x) ÷ log₁₀(b). The calculator shows both the formula and verification.
- What inputs are valid?
- Logarithm values must be positive. Bases must be positive and cannot equal 1.
