# Natural Logarithm/Examples

## 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:

$\ln 10 \approx 2 \cdotp 30258 \, 50929 \, 94045 \, 68401 \, 7991 \ldots$