The solution set of inequality log _{log (x/2)(base here is 2)}(x²-10x+22)>0

is

a. (3,5+3^1/2) U (7,infinity)

b.(3,5-3^1/2) U (7,infinity)

c.(3,3^1/2+2) U (6,infinity)

d.(3,5+3^1/2) U (8,infinity)

Answer should be b.

the following things need to be taken care of and they will give you inequalities-

1.log(x/2)should be positive and not equal to 1.

2.x²-10x+22 should be positive

3.the whole inequality should hold good which includes the cases log(x/2) greater than 1 and log(x/2) less than1.

solving the equations and inequations we can see that the answer is b.