Theory of Intelligence
9TH•Mathematics•Logarithms And Scientific Notation•2.3 Common Logarithm

2.3 Common Logarithm

Common logarithms, characteristic, mantissa, antilogarithm, and natural logarithm.

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2.3 Common Logarithm

The common logarithm is the logarithm with a base of 1010. It is written as log⁡10\log_{10} or simply as log⁡\log (when no base is mentioned, it is usually assumed to be base 1010).

For example:

101=10  ⟺  log⁡10=110^1 = 10 \iff \log 10 = 1 102=100  ⟺  log⁡100=210^2 = 100 \iff \log 100 = 2 103=1000  ⟺  log⁡1000=3and so on.10^3 = 1000 \iff \log 1000 = 3 \quad \text{and so on.} 10−1=110=0.1  ⟺  log⁡0.1=−110^{-1} = \dfrac{1}{10} = 0.1 \iff \log 0.1 = -1 10−2=1100=0.01  ⟺  log⁡0.01=−210^{-2} = \dfrac{1}{100} = 0.01 \iff \log 0.01 = -2 10−3=11000=0.001  ⟺  log⁡0.001=−3and so on.10^{-3} = \dfrac{1}{1000} = 0.001 \iff \log 0.001 = -3 \quad \text{and so on.}
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History
English mathematician Henry Briggs extended Napier's work and developed the common logarithm. He also introduced logarithmic table.

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