{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"logarithm"},"result":{"entity_type":"calculator","id":"logarithm","calculator_id":"logarithm","canonical_url":"https://tttkmbb.com/math/logarithm","name":"Logarithm Calculator","title":"Logarithm Calculator – Log to Any Base, Natural Log (ln), log₁₀ and log₂","category":"math","category_name":"Math","tool_name":"calculate_logarithm","featured_mcp_tool":false,"description":"Computes the logarithm of a positive number to any base using the change-of-base formula, and always reports the natural, common (base 10) and binary (base 2) logarithms.","use_when":"You need log_b(x) for an arbitrary base, or ln, log10 and log2 of a number at once.","do_not_use_when":"You need to raise a base to a power (use exponent) or a root (use nth-root); for pH-style −log10 of a concentration use ph.","inputs":[{"name":"value","label":"Value (x)","type":"number","required":true,"exclusive_min":0,"description":"Positive number whose logarithm is taken.","example":1000},{"name":"base","label":"Base (b)","type":"number","required":false,"default":10,"exclusive_min":0,"description":"Logarithm base; positive and not 1. Use 2.718281828459045 for the natural logarithm, or read the ln output.","example":10}],"outputs":[{"name":"log","label":"log_b(x)","type":"number","decimals":6,"description":"Logarithm of value to the given base."},{"name":"ln","label":"ln(x)","type":"number","decimals":6,"description":"Natural logarithm (base e)."},{"name":"log10","label":"log₁₀(x)","type":"number","decimals":6,"description":"Common logarithm (base 10)."},{"name":"log2","label":"log₂(x)","type":"number","decimals":6,"description":"Binary logarithm (base 2)."},{"name":"expression","label":"Expression","type":"string","decimals":4,"description":"The evaluated logarithm as text."}],"input_schema":{"type":"object","properties":{"value":{"description":"Positive number whose logarithm is taken.","type":"number","exclusiveMinimum":0,"examples":[1000]},"base":{"description":"Logarithm base; positive and not 1. Use 2.718281828459045 for the natural logarithm, or read the ln output.","type":"number","exclusiveMinimum":0,"default":10,"examples":[10]}},"additionalProperties":false,"required":["value"]},"output_schema":{"type":"object","properties":{"log":{"description":"Logarithm of value to the given base.","type":"number"},"ln":{"description":"Natural logarithm (base e).","type":"number"},"log10":{"description":"Common logarithm (base 10).","type":"number"},"log2":{"description":"Binary logarithm (base 2).","type":"number"},"expression":{"description":"The evaluated logarithm as text.","type":"string"}}},"formula":"log_b(x) = ln(x) / ln(b) (change of base); ln = log_e, log10 = log_10, log2 = log_2","sources":[{"name":"Wikipedia – Logarithm","url":"https://en.wikipedia.org/wiki/Logarithm","type":"reference","retrieved_at":"2026-09-23"},{"name":"NIST Digital Library of Mathematical Functions §4.2 – Elementary functions: definitions of the logarithm","url":"https://dlmf.nist.gov/4.2","type":"standard","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Logarithm","url":"https://mathworld.wolfram.com/Logarithm.html","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"log10 of 1000","inputs":{"value":1000,"base":10},"expected":{"log":3,"ln":6.907755,"log10":3,"log2":9.965784,"expression":"log_10(1000) = 3"},"url":"https://tttkmbb.com/api/v1/calculate/logarithm?value=1000&base=10"},{"name":"log2 of 8","inputs":{"value":8,"base":2},"expected":{"log":3,"ln":2.079442,"log10":0.90309,"log2":3},"url":"https://tttkmbb.com/api/v1/calculate/logarithm?value=8&base=2"}],"faq":[{"q":"Why can't the value be 0 or negative?","a":"Real logarithms are only defined for positive numbers: log(0) tends to −∞ and logarithms of negatives are complex."},{"q":"Which base does 'log' mean?","a":"In science and calculators 'log' usually means base 10, in mathematics often base e, and in computing base 2. All three are reported so no convention is assumed."}],"tags":["logarithm","log","natural log","ln","log base 2","log base 10"],"related":[{"calculator_id":"exponent","reason":"Inverse operation: b^y = x."},{"calculator_id":"nth-root","reason":"Roots as fractional exponents."},{"calculator_id":"ph","reason":"pH is −log10 of hydrogen-ion concentration."}],"links":{"html":"https://tttkmbb.com/math/logarithm","markdown":"https://tttkmbb.com/math/logarithm.md","json":"https://tttkmbb.com/math/logarithm.json","api":"https://tttkmbb.com/api/v1/calculate/logarithm","schema":"https://tttkmbb.com/api/v1/calculators/logarithm","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:25:35Z","next_actions":[{"tool":"run_calculator","calculator_id":"logarithm","reason":"Run Logarithm Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/math/logarithm.md"}}