Logarithm Calculator
Compute logₐ(x), ln(x), and log₁₀(x) for any positive value and base.
How it works
- 1Enter a positive value x and a valid base (positive, not equal to 1).
- 2logₐ(x) answers “a raised to what power equals x?” — computed as ln(x) ÷ ln(a) via the change-of-base identity.
- 3Results for ln(x) and log₁₀(x) are shown alongside the custom-base result for quick comparison.
Use cases
- Solving exponential equations in algebra and precalculus coursework.
- Converting between decibel (log₁₀) and neper (ln) scales in signal processing.
- Evaluating information entropy and complexity measures that use log base 2.
Frequently asked questions
Why is the result — for some inputs?
Logarithms are only defined for positive values (x > 0) and bases that are positive and not equal to 1. Any other input yields an undefined result.
What base does the natural logarithm use?
The natural logarithm uses base e ≈ 2.71828. The ln(x) column always shows this result regardless of the base you enter.
How is a custom-base logarithm computed?
The change-of-base formula converts any logarithm: logₐ(x) = ln(x) ÷ ln(a). This works for any valid positive base other than 1.
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