Natural Logarithm/Examples
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Examples of Natural Logarithm
Natural Logarithm: $\ln 2$
Mercator's constant is the real number:
\(\ds \ln 2\) | \(=\) | \(\ds \sum_{n \mathop = 1}^\infty \frac {\paren {-1}^\paren {n - 1} } n\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1 - \frac 1 2 + \frac 1 3 - \frac 1 4 + \dotsb\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 0 \cdotp 69314 \, 71805 \, 59945 \, 30941 \, 72321 \, 21458 \, 17656 \, 80755 \, 00134 \, 360 \ldots \ldots\) |
Natural Logarithm: $\ln 3$
The natural logarithm of $3$ is:
- $\ln 3 = 1.09861 \, 22886 \, 68109 \, 69139 \, 5245 \ldots$
Natural Logarithm: $\ln 10$
The natural logarithm of $10$ is approximately:
- $\ln 10 \approx 2 \cdotp 30258 \, 50929 \, 94045 \, 68401 \, 7991 \ldots$