## Appendix A |
## Errors and Uncertainties |

The absolute uncertainty in a natural log (logarithms to base *e*, usually written
as* ln *or log_{e}) is equal to a ratio of the
quantity uncertainty and to the quantity. Uncertainty in logarithms to other bases (such as common logs logarithms to base
10, written as log_{10} or simply log) is this absolute uncertainty adjusted by a
factor (divided by 2.3 for common logs). Note, logarithms do not have units.

\[ ln(x \pm \Delta x)=ln(x)\pm \frac{\Delta x}{x}\]

\[~~~~~~~~~ln((95 \pm 5)mm)=ln(95~mm)\pm \frac{ 5~mm}{95~mm}\]

\[~~~~~~~~~~~~~~~~~~~~~~=4.543 \pm 0.053\]