{
  "id": "antilog",
  "version": "2c6090c75277",
  "status": "published",
  "name": "Antilog Calculator",
  "question": "What is the antilog of a number?",
  "summary": "Raises a base to a logarithm to find the original number, or finds the log value or the base from the other two.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/antilog-calculator",
  "markdown": "https://www.acalculator.org/math/antilog-calculator.md",
  "kind": "formulas",
  "method": "x = antilog_b y = b^y, so log_b x = y.",
  "assumptions": [
    "The base is more than 0 and not 1, so the antilog is always more than 0.",
    "An old link with base=e uses Euler’s number e ≈ 2.718281828 as the base.",
    "A whole-number log value or base within float error is shown exactly."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "b": {
        "title": "Base (b)",
        "description": "The base of the logarithm: 10 for the common antilog, 2.718281828 (e) for the natural one.",
        "type": "number",
        "exclusiveMinimum": 0
      },
      "logValue": {
        "title": "Log value (y)",
        "description": "The logarithm to turn back into a number.",
        "type": "number"
      },
      "answer": {
        "title": "Antilog (x)",
        "description": "The number whose logarithm in this base is the log value: the base raised to the log value.",
        "type": "number",
        "exclusiveMinimum": 0
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "b",
      "logValue",
      "answer"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "base": {
      "label": "Base (b)",
      "description": "The base of the logarithm: 10 for the common antilog, 2.718281828 (e) for the natural one.",
      "format": "number"
    },
    "logValue": {
      "label": "Log value (y)",
      "description": "The logarithm to turn back into a number.",
      "format": "number"
    },
    "antilog": {
      "label": "Antilog (x)",
      "description": "The number whose logarithm in this base is the log value: the base raised to the log value.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "b": 10,
      "logValue": 2
    },
    "outputs": {
      "antilog": 100
    },
    "text": "The antilog of 2 in base 10 is 100."
  },
  "examples": [
    {
      "given": {
        "b": 10,
        "logValue": 2
      },
      "expect": {
        "answer": 100
      },
      "source": "hand calculation in content.mdx: 10² = 100; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "b": 2,
        "logValue": 10
      },
      "expect": {
        "answer": 1024
      },
      "source": "hand calculation in content.mdx: 2¹⁰ = 1,024; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "b": 10,
        "logValue": -2
      },
      "expect": {
        "answer": 0.01
      },
      "source": "hand calculation in content.mdx: 10⁻² = 0.01; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "b": 10,
        "logValue": 0.5
      },
      "expect": {
        "answer": 3.1622776601683795
      },
      "source": "hand calculation in content.mdx: 10^0.5 = √10 = 3.16227766…; Python 3: 10 ** 0.5 = 3.1622776601683795; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "b": 2.718281828459045,
        "logValue": 1
      },
      "expect": {
        "answer": 2.718281828459045
      },
      "source": "hand calculation in content.mdx: e¹ = e; Python 3: math.e = 2.718281828459045; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "b": 10,
        "answer": 1000
      },
      "expect": {
        "logValue": 3
      },
      "source": "hand calculation in content.mdx: 10³ = 1,000, so y = log₁₀ 1,000 = 3; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    },
    {
      "given": {
        "logValue": 2,
        "answer": 49
      },
      "expect": {
        "b": 7
      },
      "source": "hand calculation in content.mdx: b = 49^(1/2) = 7; OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions"
    }
  ],
  "sources": [
    "OpenStax, College Algebra 2e, §6.3 Logarithmic Functions. https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions",
    "NIST Digital Library of Mathematical Functions, §4.2 Definitions (logarithm, exponential, powers). https://dlmf.nist.gov/4.2"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "Base 1 and values past double range say why there is no answer."
    },
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}