Number of value(s) of `x` satisfying `log_(x^2 + 2) (5+sqrt(x)) + log_(2+sqrt(x)) (5+x^2) = 0` is/are

Find the number of values of x satisfying 2(log_(2)x)^(2)+(1-sqrt(2))log_(2)x^(2)=2sqrt(2)

The number of value(s) of x satisfying 1-log_(3)(x+1)^(2)=1/2log_(sqrt(3))((x+5)/(x+3)) is

The number of value(s) of x satisfying 1-log_9(x+1)^2=1/2log_(sqrt(3))((x+5)/(x+3)) is

The value of x satisfying log_(3)4 -2 log_(3)sqrt(3x +1) =1 - log_(3)(5x -2)

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

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

Number of value(s) of 'x' which satisfy the equation log_(3+x^(2))(15+sqrt(x))=log_(5+x^(2))((1)/(2+sqrt(x))) is/are-