logarithm
Let an agent explain logarithms and their definition, properties and bases, support calculations and use of logarithmic scales, describe applications in science, statistics and computing, and support learning.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What a logarithm is.
Concept
Definition and bases.
Concept
Concept.
- What is a logarithm, and how do common, natural and binary logarithms differ? definition
- Which base is meant? boundary
Properties
Properties.
Properties
Properties.
- What are the product, quotient, power and change of base rules, and why do they hold? definition
- Which entry fits exponentials? action
Calculate Calculation and scales.
Compute
Computing logarithms.
Compute
Computation.
- How can this logarithm be computed or an equation with logarithms solved? action
- Which entry fits solving equations? action
Scales
Logarithmic scales.
Scales
Scales.
- How do logarithmic scales such as decibels, pH and earthquake magnitude work, and how are they read? provenance
- Which entry fits a specific scale? action
Apply Applications.
Statistics
Statistics and science.
Statistics
Statistics.
- How are log-likelihood, log probability and log transformations used in statistics and science? provenance
- Which entry fits likelihood? action
Computing
Computing and cryptography.
Computing
Computing.
- How do binary logarithms describe algorithm complexity, and what is the discrete logarithm problem in cryptography? provenance
- Which entry fits computational complexity? action
Learn History and teaching.
History
History.
History
History.
- How did Napier and others develop logarithms, and how did tables and slide rules transform calculation? provenance
- Which references are standard? provenance
Teach
Teaching.
Teach
Teaching.
- How can logarithms be taught? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- logarithmic unit, log probability, log-likelihood, natural logarithm, binary logarithm, discrete logarithm, elliptic curve discrete logarithm
What it is Filled
The exponent to which a fixed base must be raised to produce a given number, the inverse of exponentiation, in forms such as the common logarithm to base ten, the natural logarithm to base e and the binary logarithm to base two, with properties turning multiplication into addition and powers into products, and extensions such as complex and discrete logarithms; logarithms underlie logarithmic scales such as decibels and pH, log-likelihood and log probability in statistics, and computation from slide rules to algorithms.
Why it exists Filled
Let an agent explain logarithms and their definition, properties and bases, support calculations and use of logarithmic scales, describe applications in science, statistics and computing, and support learning.
Distinguishing features Filled
- Inverse of powers
- Product to sum rule
- Choice of base
- Logarithmic scales
What robots and AI may and may not do Filled
Must not
- Present numerical results without stating the base when it matters.
- Mislead with a logarithmic scale presented as linear, or the reverse.
- Give results beyond the precision the input supports.
Only with a human decision
- Relying on a computed value for engineering, dosing or financial decisions.
May
- Explain logarithms, their bases, rules and uses.
- Compute logarithms and show the working.
Moral aspects Filled
- Log scales on charts can hide or exaggerate risk, for example in epidemics or earthquakes.
- Misunderstood exponential growth leads to poor public decisions.
Who is affected
- Students
- Readers of charts
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q164307 - registry parent class
- Q629085 - registry parent class
- Q864333 - registry parent class
related
- transcendental function - category
- multivalued function - category
- root - another inverse of exponentiation
- trillion - large numbers expressed on logarithmic scales
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.logarithm
- Wikidata: Q11197 (https://www.wikidata.org/wiki/Q11197)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Exponent giving a number from a base
- Common, natural, binary, discrete, complex logarithms
- An exponential is the inverse; a root is a different inverse of powers
- Not physical; a mathematical function.
Capabilities and actions required Filled
- explain definition and properties
- support calculations
- describe applications
- support learning
Hazards and failure modes required Filled
- Confusing bases
- Misreading logarithmic scales
- Domain errors with zero and negatives
Standards and interfaces required Filled
- Mathematical notation conventions
- Standards for logarithmic units such as the decibel
- Curriculum standards for algebra
Context of use required Filled
- Inverse of exponentiation.
- common logarithm
- natural logarithm
- binary logarithm
- discrete logarithm
- complex logarithm and logarithmic units
Sources Filled
- Wikidata item Q11197: logarithm - identity and sense of the item
- Wikipedia: Logarithm - general description of the item
Open questions
- Should the natural logarithm be a separate entry?
- How should textbooks be linked?
- How should scale standards be linked?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q11197/spec.json