An algorithm is a step-by-step procedure for solving a problem; a logarithm is a mathematical operation that measures a number by its order of magnitude, in powers of ten. They look and sound almost the same — the same letters jumbled — but an algorithm is a method you follow, while a logarithm is a calculation about scale.
an algorithm is something you DO (steps); a logarithm is something you CALCULATE (scale).
These two are confused for one reason only: they are near-anagrams that share a rhythm and a Greek-flavoured ending, so the eye and ear keep swapping them. Yet they come from different worlds. Algorithm honours the mathematician al-Khwārizmī and means an ordered recipe of steps — a process. Logarithm was coined by John Napier from logos ('ratio') and arithmos ('number') and names an operation that turns powers of ten into equal steps — a measure of scale. One tells you how to do something; the other tells you how big something is.
algorithm
An algorithm is a finite sequence of exact, ordered steps that turns an input into a result: do this, then this, then stop. The name is a worn-down tribute to the 9th-century mathematician al-Khwārizmī, whose rules for calculation reached medieval Europe as 'algorism'. What defines an algorithm is not cleverness but repeatability — follow the same steps in the same order and you reach the same answer every time. A recipe, a long-division method, and the strategy a search engine uses to rank pages are all algorithms. It is constantly confused with logarithm, a word that merely sounds alike.
logarithm
A logarithm answers one question: how many times must I multiply the base by itself to reach this number? The base-10 logarithm of 1000 is 3, because 10 × 10 × 10 = 1000. Coined in 1614 by John Napier from the Greek logos ('ratio') and arithmos ('number'), it turns multiplication into addition and compresses enormous ranges into a readable scale. That is why earthquakes, sound, and acidity are read on logarithmic scales, where each equal step is a tenfold jump in the real quantity — a hidden surge that the even spacing politely conceals. It rhymes with algorithm but shares none of its meaning.
| algorithm | logarithm | |
|---|---|---|
| Meaning | a step-by-step procedure to solve a problem | an operation measuring a number's order of magnitude |
| Field | computing, maths, any method | maths, science, data |
| Key axis | how to do it — a process | how big it is — a scale |
| Often with | sorting / search · run an algorithm | natural / base-10 · a logarithmic scale |
| Adjective | algorithmic | logarithmic |
| Example | a sorting algorithm | a logarithmic scale |
Hear the hidden words. AlGORITHM carries a faint 'rhythm' — a set of steps with a beat you follow in order, like dance moves. LOGARITHM starts with 'log', and a log is a record of numbers; it is about counting how many tens. Steps with a rhythm → algorithm. Counting in logs of ten → logarithm. Or simply: an algorithm is something you DO; a logarithm is something you CALCULATE.
algorithm
- iThe app uses a simple algorithm to decide which notification to send first.
- iiSorting a million names by hand is hopeless, but the right algorithm does it in seconds.
- iiiCritics want the company to reveal the algorithm that decides what each user sees.
logarithm
- iOn a logarithmic scale, the jump from 1 to 10 takes the same space as 10 to 100.
- iiEngineers use the logarithm of the signal strength to keep the numbers manageable.
- iiiThe pH scale is a logarithm, so acid at pH 3 is ten times stronger than pH 4.
They are never interchangeable: you run an algorithm and you take a logarithm. If the sentence is about a method or a set of steps, it is algorithm; if it is about scale, magnitude, or powers of ten, it is logarithm. A quick tell: 'algorithmic' describes procedures and rules, while 'logarithmic' describes scales and growth.
Both surface in TOEFL and IELTS academic reading on maths, computing and science. Use 'algorithm' for a method or set of steps ('the sorting algorithm') and 'logarithm' for the scale operation ('a logarithmic scale'). The adjectives are the giveaway: 'algorithmic' describes procedures, while 'logarithmic' describes growth and scales — handy for a logarithmic graph in Task 1. You 'run an algorithm' but 'take a logarithm'; never swap those collocations.