Estimating logarithms with College Algebra students
Rick Kreminski · International Journal of Mathematical Education in Science and Technology · 1999
Values of logarithms can be estimated using only their algebraic properties, i.e. without appeal to calculus. College algebra students can achieve estimates that are of the order of 1% error, by solving certain linear systems by hand. Improving the accuracy of the approximations naturally leads in twodirections: to larger linear systems, requiring a computer; or to least squares solutions, which can be made natural and accessible tocollege algebra students in anovel, low-dimensional geometric way. Error bounding, and comparision of the new low-dimensional, geometric least squares method with the traditional higher-dimensional approach to least squares provide useful explorations for linear algebra students. Specifically, error bounding is possible for students who (1) are able to compute the distance from a point in R k to a hyperplane; (2) understand orthogonal matrices, and the basics of the singular value decomposition of a matrix; and (3) know the Taylor series for ln (1+x).