{
  "slug": "log",
  "title": "Logarithm Calculator",
  "heading": "Log Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/log",
  "summary": "log base b of x.",
  "description": "Computes the logarithm of x to any base b using change of base.",
  "formula": null,
  "dateModified": "2026-10-03",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=log",
  "inputs": [
    {
      "id": "x",
      "label": "x",
      "kind": "number",
      "hint": null,
      "default": 1000,
      "unit": null,
      "min": null,
      "max": null
    },
    {
      "id": "base",
      "label": "Base",
      "kind": "number",
      "hint": null,
      "default": 10,
      "unit": null,
      "min": null,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "result",
      "label": "log_b(x)",
      "format": "decimal",
      "hint": null,
      "primary": true
    }
  ],
  "worked_example": {
    "inputs": [
      "x: 1000",
      "Base: 10"
    ],
    "outputs": [
      "log_b(x): 3"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter x.",
      "Enter base.",
      "Read your log_b(x) on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "x": 600,
        "base": 6
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "x": 1000,
        "base": 10
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "x": 1600,
        "base": 16
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the log calculator work?",
      "a": "Computes the logarithm of x to any base b using change of base."
    },
    {
      "q": "What do I need to enter?",
      "a": "2 values: x, and base. Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the log_b(x) result mean?",
      "a": "It is returned as a decimal number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [
    "https://www.revenuelab.fyi/toolbox/exponent"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Logarithm Calculator (https://www.revenuelab.fyi/toolbox/log)"
}