Let equation `x^(log_2 x-4)=32` has two real solutions `x_1 and x_2(x_1 > x_2),` then which of the following is correct?

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

The equation x^(log_(3)x)=(x^(3))/(9) has two solutions,say x_(1) and x_(2), with x_(1)

Let S be the set of all non-zero real numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1 and x_2 satisfying the inequality abs(x_1-x_2)lt1 . Which of the following intervals is (are) a subset(s) of S ?

The equation x^((3/4)(log_2 x)^2 + (log_2 x) - (5/4))=sqrt(2) has (1) at least one real solution (2) exactly three solutions (3) exactly one irrational solution (4) complex roots

Let Y=(log(x+1)(x^(2)-3x+2)x^(2))/((x-4)^(3)(x+5)(x-3)(x^(2)+2x+2)) then which of the following options is correct

The equation (log)_(x+1)(x- .5)=(log)_(x-0. 5)(x+1) has (A) two real solutions (B) no prime solution (C) one integral solution (D) no irrational solution