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.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
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.
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.
What it is for: Inverse of exponentiation.
It can be explain definition and properties; support calculations; describe applications; support learning.
Distinguishing features
Inverse of powers
Product to sum rule
Choice of base
Logarithmic scales
What it looks like
Not physical; a mathematical function.
How it is recognised
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
Related models
is a kind of - category
is a kind of - category
is related to - another inverse of exponentiation
is related to - large numbers expressed on logarithmic scales
In practice
Families and kinds
common logarithm
natural logarithm
binary logarithm
discrete logarithm
complex logarithm and logarithmic units
Standards and regulation
Mathematical notation conventions
Standards for logarithmic units such as the decibel
Curriculum standards for algebra
Failure modes and hazards
Confusing bases
Misreading logarithmic scales
Domain errors with zero and negatives
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a logarithm is.
Mathematics.
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.
Practice.
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.
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.
Education.
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
What the second pass must settle
- Should the natural logarithm be a separate entry?
- How should textbooks be linked?
- How should scale standards be linked?