Write a C program that uses Newton's Method to solve an equation in one variable.

Try solving x^x = ln2

the deriviative of x^x is x^x(lnx + 1). The 'ln' function in C is log(), and the value

for ln2 is approximately .693147180559945 (to 15 places, about the limit of double precision).

Test for convergence using a tolerance of about 1e-10 (that is, look at the absolute value of

new_x - old_x and require this to be less than 1e-10 to say it has converged). Also keep a count

of the number of iterations; if this goes over 100, announce that there is no convergence. Otherwise

once you have convergence, print the solution (say to 15 places) and the number of iterations