TableOfCommonLogarithms 2008-06-14 16:59:39 2008-06-14 16:59:39 Data Structure Briggsian logarithms % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here This table is for integers in the range $-1 < n < 100$. To find the common logarithm (that is, with base 10, the same base of our numeral system) for the desired $n$, look for the ten's place digit (0 in the case of $-1 < n < 10$) in the leftmost column and the one's place digit in the topmost row. The intersection $x$ of that row and column thus gives $\log _{10} n$ to four or five decimal places. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} $n$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 0 & $-\infty$ & 0.00000 & 0.30103 & 0.477121 & 0.60206 & 0.69897 & 0.778151 & 0.845098 & 0.90309 & 0.954243 \\ 1 & 1. & 1.04139 & 1.07918 & 1.11394 & 1.14613 & 1.17609 & 1.20412 & 1.23045 & 1.25527 & 1.27875 \\ 2 & 1.30103 & 1.32222 & 1.34242 & 1.36173 & 1.38021 & 1.39794 & 1.41497 & 1.43136 & 1.44716 & 1.4624 \\ 3 & 1.47712 & 1.49136 & 1.50515 & 1.51851 & 1.53148 & 1.54407 & 1.5563 & 1.5682 & 1.57978 & 1.59106 \\ 4 & 1.60206 & 1.61278 & 1.62325 & 1.63347 & 1.64345 & 1.65321 & 1.66276 & 1.6721 & 1.68124 & 1.6902 \\ 5 & 1.69897 & 1.70757 & 1.716 & 1.72428 & 1.73239 & 1.74036 & 1.74819 & 1.75587 & 1.76343 & 1.77085 \\ 6 & 1.77815 & 1.78533 & 1.79239 & 1.79934 & 1.80618 & 1.81291 & 1.81954 & 1.82607 & 1.83251 & 1.83885 \\ 7 & 1.8451 & 1.85126 & 1.85733 & 1.86332 & 1.86923 & 1.87506 & 1.88081 & 1.88649 & 1.89209 & 1.89763 \\ 8 & 1.90309 & 1.90849 & 1.91381 & 1.91908 & 1.92428 & 1.92942 & 1.9345 & 1.93952 & 1.94448 & 1.94939 \\ 9 & 1.95424 & 1.95904 & 1.96379 & 1.96848 & 1.97313 & 1.97772 & 1.98227 & 1.98677 & 1.99123 & 1.99564 \\ \end{tabular}