1, a tlna-a = 0, because a≠0, so a (t- 1) = 1/lna, the natural logarithm of both sides is: (t- 1)lna =-lna.

So t= 1-lnlna/lna.

This is a test of eyesight. Obviously, x= 1 is one of the solutions of the equation, so there is a factor (x- 1), and the next step is natural.

3,4: These two problems are constructors, and then Lagrange theorem can be used.