All tools · 📊 Math
log Logarithm Calculator
Compute the logarithm of x in any base. Common presets: log₁₀ (common log), ln (natural log, base e), log₂ (binary). Useful for solving exponential equations, dB calculations, and information theory.
Examples
log₁₀(1000)3ln(e)1log₂(1024)10log₃(81)4Frequently asked questions
What is "ln" and how is it different from "log"?
ln is natural log (base e ≈ 2.71828). Plain "log" usually means base 10 in engineering, base e in pure math, or base 2 in CS — context matters.
Why log(0) error?
log(0) is negative infinity (the function diverges). Logs of negative numbers are complex; we display the complex result with imaginary part π.
Change of base formula?
log_b(x) = ln(x) / ln(b). All calculators internally convert to one base.
About this tool
Logarithm Calculator runs entirely in your browser using standard Web APIs. No data is sent to any server. The source for this tool is in our public GitHub repository.
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Why this tool
vs typical free web-tool sites
| 1vw | Typical free site | |
|---|---|---|
| Price | Free | Free |
| Signup required | No | Often (for premium features) |
| Ads inside the tool | No | Yes (banner + video) |
| Data sent to server | No (browser-only) | Yes (inputs analyzed for ads) |
| Total tools | 96 | Often <20 or scattered across sites |
| Bookmarkable URL per tool | Yes | Mixed |
| Loads in under 1s | Yes (static) | Often slow (ad tracking) |
| Multilingual | EN / ES / PT / FR / DE | Usually EN only |
| Open source | Yes | No |