Common Logarithm/Examples/2360

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Example of Common Logarithm

The common logarithm of $2360$ is:

$\log_{10} 2360 = 3 \cdotp 3729$


Proof

\(\ds 2360\) \(=\) \(\ds 2 \cdotp 36 \times 10^3\) using scientific notation
\(\ds \leadsto \ \ \) \(\ds \log_{10} 2360\) \(=\) \(\ds \map {\log_{10} } {2 \cdotp 36 \times 10^3}\)
\(\ds \) \(=\) \(\ds \log_{10} 2 \cdotp 36 + \log_{10} 10^3\) Logarithm of Product
\(\ds \) \(=\) \(\ds 0 \cdotp 3729 + 3\) Common Logarithm of $2 \cdotp 36$, Definition of Common Logarithm
\(\ds \) \(=\) \(\ds 3 \cdotp 3729\)

$\blacksquare$


Sources