Common Logarithm/Examples/0.236

Example of Common Logarithm

The common logarithm of $0 \cdotp 236$ is:

$\log_{10} 0 \cdotp 236 = \overline 1 \cdotp 3729 = -0.6271$

Proof

\(\ds 0 \cdotp 236\)

\(=\)

\(\ds 2 \cdotp 36 \times 10^{-1}\)

using scientific notation

\(\ds \leadsto \ \ \)

\(\ds \log_{10} 0 \cdotp 236\)

\(=\)

\(\ds \map {\log_{10} } {2 \cdotp 36 \times 10^{-1} }\)

\(\ds \)

\(=\)

\(\ds \log_{10} 2 \cdotp 36 + \log_{10} 10^{-1}\)

Logarithm of Product

\(\ds \)

\(=\)

\(\ds 0 \cdotp 3729 + \paren {-1}\)

Common Logarithm of $2 \cdotp 36$, Definition of Common Logarithm

\(\ds \)

\(=\)

\(\ds \overline 1 \cdotp 3729\)

Notation for Negative Logarithm

\(\ds \)

\(=\)

\(\ds -0.6271\)

$\blacksquare$

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Logarithms: Example 3.