Logarithm Calculator
Compute logs in any base — 2, e, 10 or custom. Calculate logarithms in base 2, natural log (base e), base 10 or any custom base. Handles decimals and shows the exact expression. Free log calculator.
About the Logarithm Calculator
Logarithms answer "what power turns the base into this number?" — the reverse of exponentiation and the backbone of pH values, decibels, earthquake magnitudes, algorithm complexity and compound growth. Enter a number and choose base 2, e (natural log), 10 (common log) or a custom base; the calculator returns the result to high precision and shows which expression it evaluated, so you can verify it against a textbook answer.
How to use the Logarithm Calculator
- Enter the number (must be positive).
- Choose the logarithm base.
- Read the result and the expression shown.
- Switch bases to compare values.
Key features
- Base 2, natural (e) and common (base 10) logs
- Any custom base you need
- High-precision results
- Shows the evaluated expression
Why can’t I take the log of zero or a negative number?
What is the change-of-base rule?
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