Logarithm

In mathematics, a logarithm is a function that gives the in the equation bn = x. It is usually written as logb x = n. For example:

Trivia

Unicode glyph

log has its own Unicode glyph: ㏒ (U+33D2 or 13266 in decimal). This is more likely due to its presence in Asian legacy encodings than its importance as a mathematical function.

Related Topics:
Unicode - Glyph - Decimal - Legacy encoding

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Alternate notation

A few people use the notation blog(x) instead of logb(x).

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Relationships between binary, natural and common logarithms

In particular we have:

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: log2(e) ≈ 1.44269504

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: log2(10) ≈ 3.32192809

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: loge(10) ≈ 2.30258509

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: loge(2) ≈ 0.693147181

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: log10(2) ≈ 0.301029996

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: log10(e) ≈ 0.434294482

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A curious coincidence is the approximation log2(x) ≈ log10(x) + ln(x), accurate to about 99.4% or 2 significant digits; this is because 1/ln(2) − 1/ln(10) ≈ 1 (in fact 1.0084...). The property is demonstrated in all six conversion factors above, arranged in pairs of two:

Related Topics:
Approximation - Significant digit

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This comes on top of the reciprocal relations we have:

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Another interesting coincidence is that log10(2) ≈ 0.3 (the actual value is about 0.301029995); this corresponds to the fact that, with an error of only 2.4%, 210 ≈ 103

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(i.e. 1024 is about 1000; see also Binary prefix).

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