Interval satisfying the inequality `log_(1/2) (1/2+sinx)leq 0` is equal to (where `x in [-pi,pi])`

The set of real values of x satisfying the inequality log_(x+1/x)(log_2((x-1)/(x+2))) gt 0, is equal to

The set of real values of x satisfying the inequality log _(x+(1)/(x))(log_(2)((x-1)/(x+2)))>0, is equal to

Number of values of x satisfying the equation log_(2)(sin x)+log_((1)/(2))(-cos x)=0 in the interval (-pi,pi), is equal to -

The number of value(s) of x in the interval [0,5pi] satisfying the inequation 3sin^(2)x - 7 sinx +2 lt 0 such that sinx is an integer is

If x satisfies the inequality log_(x+3)(x^(2)-x)<1 then x may belong to the interval

The value of x, satisfying the equation log_(cos x ) sin x =1 , where 0 lt x lt (pi)/(2) , is

The solution of the inequality log_(1//2)sinx gt log_(1//2)cosx in [0, 2pi] is

2.The value of x satisfying the equation log_(cos x)sin x=1 , where 0< x < (pi)/2 is

Let alpha=pi/3 , then the solution set of the inequality log_(sinalpha)(2-cos^2x)lt log_(sinalpha)(1-sinx) , where x in (0,2x) and x ne pi/2 , is