{"query": "pH — the logarithm of the proton", "count": 20, "results": [{"id": "card_n_789214dd088e", "title": "pH — the logarithm of the proton", "shelf": "science", "surface": "secular", "snippet": "pH = −log₁₀[H⁺]: acidity is literally a logarithm, so each unit is a tenfold change in\nproton concentration — pH 4 is ten times more acidic than pH 5, a hundred times more than\npH 6. Sealed in-domain:"}, {"id": "card_c_9d6917fca9f5", "title": "pH — the logarithm of the proton ↔ Logarithms — multiplication made addition, a", "shelf": "connections", "surface": null, "snippet": "−log₁₀(10⁻⁴) = 4 sealed on the logarithm card. This is chemistry borrowing the grammar of the senses  — a concord the card itself states; mined + verified."}, {"id": "card_src_word_napierian_logarithm", "title": "napierian logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "napierian logarithm: (noun) a logarithm to the base e — syn: natural logarithm"}, {"id": "card_src_word_natural_logarithm", "title": "natural logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "natural logarithm: (noun) a logarithm to the base e — syn: Napierian logarithm"}, {"id": "card_c_857eed5a5e82", "title": "Logarithms — multiplication made addition, a ↔ pH — the logarithm of the proton", "shelf": "connections", "surface": null, "snippet": "All sealed: ... acidity by pH (-log10(10^-4) = 4).  — a concord the card itself states; mined + verified."}, {"id": "card_src_word_common_logarithm", "title": "common logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "common logarithm: (noun) a logarithm to the base 10"}, {"id": "card_src_oeis_a002162", "title": "A002162 — Decimal expansion of the natural logarithm of 2.", "shelf": "oeis", "surface": "secular", "snippet": "Decimal expansion of the natural logarithm of 2.  First terms: 6, 9, 3, 1, 4, 7, 1, 8, 0, 5, 5, 9, 9, 4, 5, 3, 0, 9, 4, 1, 7, 2, 3, 2."}, {"id": "card_src_word_ph", "title": "ph", "shelf": "dictionary", "surface": "secular", "snippet": "ph: (noun) (from potential of Hydrogen) the logarithm of the reciprocal of hydrogen-ion concentration in gram atoms per liter; provides a measure on a scale from 0 to 14 of the acidity or alkalinity o"}, {"id": "card_c_60eaf1dc310a", "title": "The logarithm inverts radioactive decay", "shelf": "connections", "surface": null, "snippet": "Half-life is a logarithm of the surviving fraction — the carbon clock read backward."}, {"id": "card_src_word_ph_scale", "title": "ph scale", "shelf": "dictionary", "surface": "secular", "snippet": "ph scale: (noun) (from potential of Hydrogen) the logarithm of the reciprocal of hydrogen-ion concentration in gram atoms per liter; provides a measure on a scale from 0 to 14 of the acidity or alkali"}, {"id": "card_src_oeis_a001179", "title": "A001179 — Leonardo logarithm of n.", "shelf": "oeis", "surface": "secular", "snippet": "Leonardo logarithm of n.  First terms: 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1."}, {"id": "card_src_oeis_a002285", "title": "A002285 — Decimal expansion of common logarithm of e.", "shelf": "oeis", "surface": "secular", "snippet": "Decimal expansion of common logarithm of e.  First terms: 4, 3, 4, 2, 9, 4, 4, 8, 1, 9, 0, 3, 2, 5, 1, 8, 2, 7, 6, 5, 1, 1, 2, 8."}, {"id": "card_src_oeis_a002391", "title": "A002391 — Decimal expansion of natural logarithm of 3.", "shelf": "oeis", "surface": "secular", "snippet": "Decimal expansion of natural logarithm of 3.  First terms: 1, 0, 9, 8, 6, 1, 2, 2, 8, 8, 6, 6, 8, 1, 0, 9, 6, 9, 1, 3, 9, 5, 2, 4."}, {"id": "card_src_oeis_a002392", "title": "A002392 — Decimal expansion of natural logarithm of 10.", "shelf": "oeis", "surface": "secular", "snippet": "Decimal expansion of natural logarithm of 10.  First terms: 2, 3, 0, 2, 5, 8, 5, 0, 9, 2, 9, 9, 4, 0, 4, 5, 6, 8, 4, 0, 1, 7, 9, 9."}, {"id": "card_c_6b353b6912b0", "title": "The logarithm inverts the capacitor's exponential clock", "shelf": "connections", "surface": null, "snippet": "Exponential rises by multiplying; the logarithm returns by adding. One law, two directions."}, {"id": "card_src_oeis_a002390", "title": "A002390 — Decimal expansion of natural logarithm of golden ratio.", "shelf": "oeis", "surface": "secular", "snippet": "Decimal expansion of natural logarithm of golden ratio.  First terms: 4, 8, 1, 2, 1, 1, 8, 2, 5, 0, 5, 9, 6, 0, 3, 4, 4, 7, 4, 9, 7, 7, 5, 8."}, {"id": "card_n_5d1c28bd4ea5", "title": "Logarithms — multiplication made addition, and the grammar of the senses", "shelf": "science", "surface": "secular", "snippet": "The logarithm turns multiplication into addition: log(15) = log(3)+log(5), sealed. That\none property made calculation possible before computers (Napier 1614 -> slide rules -> every\nengineer until 1970"}, {"id": "card_src_word_logarithm", "title": "logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "logarithm: (noun) the exponent required to produce a given number — syn: log"}, {"id": "card_src_word_proton", "title": "proton", "shelf": "dictionary", "surface": "secular", "snippet": "proton: (noun) a stable particle with positive charge equal to the negative charge of an electron"}, {"id": "card_src_oeis_a002164", "title": "A002164 — E.g.f.: high-temperature series in J/2kT for logarithm of partition function for the spin-1/2 linear (1D) Heisenberg model.", "shelf": "oeis", "surface": "secular", "snippet": "E.g.f.: high-temperature series in J/2kT for logarithm of partition function for the spin-1/2 linear (1D) Heisenberg model.  First terms: 0, 3, -6, -30, 360, 504, -44016, 204048, 8261760, -128422272, "}]}