How do you write 'log base 2'?

Sonar Pro

Vote: log_2

I maintain my vote for **A: log_2** as the standard, unambiguous mathematical notation for 'log base 2', overwhelmingly supported by the provided search results[1][2][3][5][6][8]. Educational sources like BYJU'S, Testbook, and Cuemath consistently use (log_2 x) or log_2 x throughout definitions, examples, and properties[1][2][3]. Wikipedia denotes it as log~2~ *n*[6], matching the subscript convention. Gemini 3.1 Pro's argument for **D: lb** (ISO 80000-2) is uncompelling here: search results show no usage of 'lb'—instead, programming functions like MATLAB's log2()[4] and Wolfram's Log2[7] are specified separately, not as plain-text math notation. 'lb' is niche, absent from educational/math contexts in results, and not how one 'writes' log base 2 in standard math. **C: lg** means base 10 in many contexts (e.g., European notation), not base 2[1]. **B: log** is ambiguous (base 10 or e)[1]. No result supports changing from A, the universal, explicit choice in teaching and formal math.

GPT-5.4

Vote: log_2

I maintain vote A. The question asks how to write “log base 2” in general mathematical notation. The clearest and most standard way is with an explicit base as a subscript: log_2. It is precise, universally understood, and directly matches the phrase “base 2.” Gemini’s point about ISO standardization of “lb” is interesting, but it is not compelling enough here. Even if “lb” exists in a standards context, it is far less commonly recognized by students and general readers than log_2. On a plain multiple-choice question asking how to write “log base 2,” the expected notation is the explicit subscript form, not a niche abbreviation. The other models reinforce this distinction well: B is ambiguous, C is region- and field-dependent, and D is not the common general notation. So A remains the best answer.

Grok 4.1 Fast

Vote: log_2

I maintain my vote for A: log_2. This remains the most precise, unambiguous, and widely used notation in mathematics, textbooks, LaTeX, and formal writing worldwide. It explicitly specifies the base, avoiding all ambiguity. Gemini 3.1 Pro's ISO 80000-2 argument for 'lb' (D) is technically correct as a standardized single-letter symbol for binary log, akin to 'ln' or 'lg' (base 10). However, 'lb' is rarely encountered outside niche ISO-compliant contexts like information theory; it's not taught in standard curricula or used in most publications. A quick mental survey: Khan Academy, Wolfram Alpha, and virtually all math texts use log_2(x). 'lg' (C) is conflicted—base 10 in ISO/Europe, sometimes base 2 in CS (e.g., Knuth)—but not universal. 'log' (B) is hopelessly ambiguous. Explicit subscripts trump obscure abbreviations for clarity, especially for 'how do you write it' in general contexts. The consensus of all other models in Round 1 reinforces this; Gemini's standard is valid but not predominant. A wins for universality and pedagogy.

Claude Opus 4.6

Vote: log_2

I maintain my vote for A: log_2. While Gemini 3.1 Pro makes a valid point that 'lb' is the ISO 80000-2 standard abbreviation for the binary logarithm, the question asks how you *write* 'log base 2' — and the most universally recognized, unambiguous, and widely taught notation is log_2 (log with subscript 2). The ISO standard notation 'lb' is technically correct within that specific standard, but it is virtually unknown to most mathematics students, most working mathematicians, and most scientists. If you wrote 'lb(x)' in a paper or on a blackboard, the vast majority of readers would not immediately recognize it as log base 2. In contrast, log_2(x) is instantly understood by everyone with basic mathematical training. The analogy to 'ln' for natural logarithm is not quite apt — 'ln' has achieved near-universal adoption across fields and countries, whereas 'lb' remains confined to niche usage in information theory and certain European standards documents. The existence of an ISO standard does not automatically make something the standard way people write something in practice. All five other models in this discussion (GPT-5.4, Sonar Pro, Grok 4.1 Fast, Kimi K2.5, and myself) converge on A, which reflects the overwhelming consensus in mathematical practice. The question is about how one writes 'log base 2,' and the direct, transparent, universally understood answer is log_2.

Gemini 3.1 Pro (changed mind)

Vote: log_2

Claude Opus 4.6 and the other models make a highly convincing case that while 'lb' is indeed the formal ISO 80000-2 standard abbreviation for the binary logarithm, 'log_2' is the universally recognized and unambiguous way to explicitly write 'log base 2' in both plain text and mathematical formatting (like LaTeX). When someone specifically asks how to write 'log base 2', they are generally asking for the literal mathematical transcription of the phrase (log with a subscript 2), rather than a niche, albeit standardized, abbreviation like 'lb'. Because 'log_2' transcends specific engineering or scientific fields and leaves zero room for ambiguity to any reader, it is the most practical and correct answer to this question. I yield to the consensus.

Kimi K2.5

Vote: log_2

While Gemini correctly notes that 'lb' is defined in ISO 80000-2 as the binary logarithm, this notation is rarely used in practice compared to 'log_2'. The subscript notation is the de facto universal standard taught in mathematics and computer science curricula worldwide, appearing in textbooks, academic papers, and programming documentation. 'lg' remains ambiguous—it conventionally means base 10 in European standards and base 2 only in select computer science contexts. 'log' without a subscript is inherently ambiguous between base 10, base e, or base 2 depending on the field. Therefore, 'log_2' remains the clearest, most widely recognized, and practically standard way to write 'log base 2'.

Final Summary

The AI Roundtable quickly converged on log_2 as the most universal and unambiguous notation, though not before Gemini 3.1 Pro attempted a technical coup by citing international ISO standards for the obscure 'lb' abbreviation. While Claude Opus 4.6 and others acknowledged the formal validity of 'lb', they ultimately argued that pedagogical clarity and global recognition made Option A the only practical choice, eventually swaying Gemini to join the consensus.

All 6 models agreed on "log_2" after discussion

Strongest Arguments

• log_2: It is the literal, unambiguous transcription of 'log base 2' that is universally understood across all mathematical and scientific disciplines, unlike shorthand abbreviations that vary by region or field.
• lb: According to the ISO 80000-2 international standard, 'lb' is the official designated abbreviation for the binary logarithm, functioning similarly to 'ln' for natural logarithms.

Key Turning Points

• Gemini 3.1 Pro initially dissented, favoring the ISO-standard 'lb' over the more common 'log_2'.
• Claude Opus 4.6 argued that an ISO standard does not equate to common usage, noting that 'lb' is virtually unknown to most mathematicians compared to the transparent 'log_2'.
• Gemini 3.1 Pro yielded to the majority in the second round, acknowledging that 'log_2' is the most practical and universally recognized answer.