Logarithm
A logarithm is the exponent to which a specified positive base other than one must be raised to produce a given positive number.
Statistics Every Programmer Needs
A logarithm is the exponent to which a specified base must be raised to obtain a given number.
- How it is used
- Uses base-10 logarithms to calculate Benford probabilities and transform numeric data for leading-digit analysis.
- How deep it goes
- Defines logarithmic scales and mantissas, then demonstrates Python calculations and statistical checks without developing proofs.
- Examples
- Demonstrates digit probabilities, population logarithms, mantissa extraction, summary statistics, and ranked mantissa plots.
- What you can do after
- Apply via NumPy to calculate base-10 logarithms, derive mantissas, and evaluate Benford-style numeric data.
Read how Statistics Every Programmer Needs explains logarithm →
Math for Web Design
A logarithm is the exponent to which a base must be raised to produce a specified number.
- How it is used
- Uses log() to calculate a graduated CSS font-size scale from numeric steps.
- How deep it goes
- Defines logarithms through a base-and-exponent example, then applies log() in a CSS calculation.
- Examples
- Demonstrates log(8, 2) = 3 and a heading scale with steps from 0 to 12.
- What you can do after
- Apply it via CSS log() and calc() to build a logarithmic font-size scale.
Grokking Data Structures
A logarithmic function grows proportionally to the logarithm of its input and therefore increases very slowly as input size grows.
- How it is used
- Uses logarithmic growth to compare how algorithm resources scale as input size increases.
- How deep it goes
- Defines slow growth and compares growth classes, stopping short of deriving logarithmic formulas or algorithm implementations.
- Examples
- Compares array searching, heapsort, pair generation, and subarray generation through estimated asymptotic running times.
- What you can do after
- Evaluate/understand an algorithm’s approximate order of growth and distinguish slow scaling from rapidly accelerating alternatives.
Related concepts
- binary searchused by · Binary search is an algorithm that locates a target or boundary in an ordered collection by repeatedly comparing with a midpoint and halving the remaining search range.
- Zipf's lawconfigured by · Zipf's law is an empirical statistical law stating that an item's frequency in a ranked distribution is approximately inversely proportional to its rank.
- mantissahas part · A mantissa, more precisely called a significand, is the component of a scientific-notation or floating-point representation that carries a number’s significant digits or bits.
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