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  "api": "https://www.calculatorx.com/api/v1/calc/ln",
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  "assumptions": [
    "Real arithmetic; argument x > 0. Base is e, not 10.",
    "On many calculators log means log₁₀; in some programming languages log(x) means ln(x).",
    "Published engine is y = ln(x). A legacy y query parameter is ignored and stripped from the address bar. Inverse x = e^y is Antilog with base e."
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  "limitations": [
    "Positive finite binary64 x or symbolic e; strict decimal/scientific text ≤512 characters; nonzero text rounded to zero rejects NUMERIC_UNDERFLOW. Unknown keys/conflicting x aliases reject. Legacy y/yInput ignored.",
    "Math.log approximates normalized binary64 inputs. Exact flag only x=1 or symbolic e. Display 12 significant digits; native exports retain full pack and input text.",
    "Independent Decimal180 vectors accept logarithms within4 ULP and inverse values within16 EPS max(1,|y|) relative plus2 subnormal quanta. Existing16 O3 vectors retain2 ULP; neither claim covers the whole domain.",
    "Near1 input rounding is ill conditioned; inverse check tolerance128 EPS max(1,|y|) relative plus2 subnormal quanta is not exactness proof.",
    "Typing local; shared URLs/REST/MCP send inputs and may enter logs. Slider0.1–10 only; Focus graph bounded around current input."
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    "x ≤ 0 returns INVALID_ARGUMENT (real ln is undefined).",
    "x = 1 returns 0 (exact). Only symbolic e returns 1 with the exact flag. Numeric Math.E rounds to 1 without that flag; it is a rounded approximation of the mathematical constant e.",
    "0 < x < 1 yields a negative result (for example ln(0.5) = −ln(2)).",
    "For every finite x > 0 in binary64, y = ln(x) is finite (about −744 < y < 710). Domain errors use INVALID_ARGUMENT; the engine does not return Infinity for valid positive finite inputs."
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      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Logarithm, Exponential, Powers",
      "url": "https://dlmf.nist.gov/4",
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      "section": "Logarithm: definitions and inverse of the exponential",
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      "supports": "e^(ln x) = x and ln(e^y) = y for real x > 0",
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      "publisher": "National Institute of Standards and Technology"
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      "section": "Natural logarithm base e; real argument x > 0",
      "supports": "This page is ln only. Common log is the Log calculator; inverse is Antilog with base e.",
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