>>14327522The analytical way would be:
Assume a solution exists. Then let . Then . Another way of writing this would be . From that form, we know that the function on the left is monotonic and is only defined for . Therefore if a solution exists (for y) it must be positive and unique. Because this function is also continuous we know that unique solution must exist because and . Therefore the solution exists, it's unique and can be computed via Newton's method. We already know it's first digit must be 1. If you want more digits, go ahead and do Newton's method.
We must now solve
Same reasoning as before, the solution exists, is unique and it's first digit is one.
The solution is 1. ...
If you want more digits feel free to do Newton's method.
