kill(all)$

van=facebook.com/LearningCalculus$

y(x):=(sqrt(2)*cos(x)+1)^2+7;

f(x,y):=sqrt(y-7)=sqrt(2)*cos(x)+1;

assume(sqrt(2)*cos(x)+1>0);

solve(f(x,y),y);

Log(a,u):=log(u)/log(a)$

(2*Log(2,sin(x))^2 + 3*Log(2,sin(x))) /
   Log(3,-cos(x));

solve(%,x);