Common Logarithm/Examples/657.3

Example of Common Logarithm

The common logarithm of $657 \cdotp 3$ is:

$\log_{10} 657 \cdotp 3 = 2 \cdotp 8178$

Proof

\(\ds 657 \cdotp 3\)

\(=\)

\(\ds 6 \cdotp 573 \times 10^2\)

using scientific notation

\(\ds \leadsto \ \ \)

\(\ds \log_{10} 657 \cdotp 3\)

\(=\)

\(\ds \map {\log_{10} } {6 \cdotp 573 \times 10^2}\)

\(\ds \)

\(=\)

\(\ds \log_{10} 6 \cdotp 573 + \log_{10} 10^2\)

Logarithm of Product

\(\ds \)

\(=\)

\(\ds 0 \cdotp 8178 + 2\)

Common Logarithm of $6 \cdotp 573$, Definition of Common Logarithm

\(\ds \)

\(=\)

\(\ds 2 \cdotp 8178\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logarithm (log)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logarithm (log)