Solve the inequality `sqrt((log)_2((2x-3)/(x-1)))<1`

Solve the inequality 3(x-145) le 2(x-3)

Solve the inequality (3x-4)/(2) ge (x+1)/(4)-1 .

The inequality sqrt(x^((log)_2sqrt(x)))geq2 is satisfied by (A) only one value of x (B) x in [0,(1/4)] (C) x in [4,oo] (d) x in (1,2)

Solve the inequality sin2x gtsqrt(2)sin^2x+(2-sqrt(2))cos^2x

Solve: (log)_2((x^2+1)/(x-1))<0

Solve the inequality 2(2x+3)-10 lt 6(x-2) , when x is a real number.

The solution of the inequality (log)_(1/2sin^(-1)x >(log)_(1//2)cos^(-1)x is x in [(0,1)/(sqrt(2))] (b) x in [1/(sqrt(2)),1] x in ((0,1)/(sqrt(2))) (d) none of these

Number of integers lt=10 satisfying the inequality 2(log)_(1/2)(x-1)lt=1/3-1/((log)_(x^2-x)8) is............