kill(all)$

van=facebook.com/LearningCalculus$

f(x):=(x^2-6*x+6)^(x^2-2);

g(x):=(x^2-6*x+6)^(4*x-5);

F(x):=(x^2-2);

G(x):=(4*x-5);

solve(F(x)=G(x),x);

[[1, f(1)],[3,f(3)],[1,F(1)],[3,F(3)]];

[[5,f(5)],[5,g(5)]];