Logarithms by Interpolation

Extract

The method of introducing logarithms given in the Algebra Report consists in taking the powers of 1·1, which are easily calculated and are so closely packed that common logarithms can be deduced by proportional parts correct to three decimal places. It forms an interesting set of lessons for post-certificate pupils to discuss why this is so, and to extend the method with a view to obtaining greater accuracy Furthermore, one of the most important principles in pure mathematics is amply illustrated—that of sandwiching a function between two bounds. It is assumed that the expansion of log_e(l + x) is known by the pupils and also its differential coefficient.