Number of solutions of x `in[0,pi]` satisfying the equations `(log_(sqrt3)tanx)(sqrt(log_(sqrt3)3sqrt3+log_(tanx)3))=-1` is/are_____

Find the number of solution of theta in[0,2 pi] satisfying the equation ((log)_(sqrt(3))tan theta(sqrt((log)_(tan theta)3+(log)_(sqrt(3))3sqrt(3))=-1

The number of solutions of theta in [0,2pi] satisfying the equation log_(sqrt(5))tan theta sqrt(log_(tan theta)5sqrt(5)+log_(sqrt(5))5sqrt(5))=-sqrt(6) is ____________.

Number of value(s) of 'x' satisfying the equation x^(log_(sqrt(x))(x-3))=9 is/are

Sum of the values of x satisfying the equation log_(3)(5x-6)log_(x)sqrt(3)=1 is

The number of values of x satisfying the equation log_(2)(log_(3)(log_(2)x)))>=sqrt(8-x)+sqrt(x-8) is :

The number of real values of x satisfying the equation log_(10) sqrt(1+x)+3log_(10) sqrt(1-x)=2+log_(10) sqrt(1-x^(2)) is :

The equation x[(log_(3)x)^(2)-(9)/(2)log_(3)x+5]=3sqrt(3) has