 
			
		
					 
						
									In this paper we study the sequence

of iterated exponentials by a, a > 0; as well as the range of solvability of the equations

We state that these two problems are closely related with the behavior of the functions

and with the old problem of finding the solutions of the equation  . Finally, we study the behavior of the function.
. Finally, we study the behavior of the function.

calculate its inverse and draw its graph.