Given a > 0, we wish to compute x = lna using addition, subtraction, multiplication, division, and the exponential function, ex.
(a) Suggest an iterative formula based on Newton's method, and write it in a way suitable for numerical computation.
(b) Show that your formula converges quadratically.
(c) Write down an iterative formula based on the secant method.
(d) State which of the secant and Newton's methods is expected to perform better in this case in terms of overall number of exponential function evaluations. Assume a fair comparison, i.e., same floating point system, "same quality" initial guesses, and identical convergence criterion.