Appendix A

Errors and Uncertainties

Course Support
Lab Contents

Natural Logarithms

The absolute uncertainty in a natural log (logarithms to base e, usually written as ln or loge) 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 log10 or simply log) is this absolute uncertainty adjusted by a factor (divided by 2.3 for common logs). Note, logarithms do not have units.

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

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

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