Solving advanced mathematics problems: sinx=lnx, x=?

The numerical solution with matlab is 2.2 19 1.

Upstairs kindly answer why it's not nice.

First of all, transcendental equation has no analytical solution and can only be solved numerically. There are many algorithms for finding numerical solutions, and Newton method is one of them. This is a method of approaching the true value by using the limit of sequence. You can use any math software you want to solve, such as matlab and mathematic.

Taylor series expansion is a joke, let alone McLaughlin expansion. Lnx is not defined at 0: 00. How to extend with mclaughlin? These expansions are only approximations near a certain point, and you have no idea what the solution is. At this point, how can you extend the solution? And if it can't be expanded at this point, how can it be an exact solution?