Problems of the form a^b=1

Problem: Find solutions to (2-x^2)^(x^2-3*sqrt(2)x+4)=1

First, find solutions assuming x is real. Then, find solutions assuming x is complex.

Solution: x^y=1 has solutions x=1, y=anything, or x=anything but 0 or 1, y=(i 2pi n)/log(x)

The first solution of (2-x^2)^(x^2-3*sqrt(2)x+4)=1 is (2-x^2)=1, so x=-1 or x=1

The second solution of (2-x^2)^(x^2-3*sqrt(2)x+4)=1 is (x^2-3*sqrt(2)x+4)=(i 2pi n)/log(2-x^2) (x^2-3*sqrt(2)x+4)log(2-x^2)=i*2*pi*n