Consider the inequalities `log_5(x-3)+1/2log_5 3<1/2log_5(2x^2-6x+7)and log_(3)x+log_(sqrt(3))x+log_(1/3)x<6.`

Consider the inequalities log_(5)(x-3)+(1)/(2)log_(5)3<(1)/(2)log_(5)(2x^(2)-6x+7) and log_(3)x+log_(sqrt(3))x+log_((1)/(3))x<6

Find the sum of all integers satisfying the inequalities log_(5)(x-3)+1/2log_(5)3lt1/2log_(5)(2x^(2)-6x+7) and log_(3)x+log_(sqrt3)x+log_(1/3)xlt6

Solve the following inequalities : log_(1//2)log_3((x+1)/(x-1))ge0

Solve the inequality log _(0.5)|1x|log_(x1)2<=2

Solve the following inequalities : log_(0.5)(x+5)^2gt log_(1//2)(3x-1)^2

The number of integral value of x satisfying the following system of inequalities (sqrt(log_(2)^(2)x-3log_(2)x+2))/(log_(5)((1)/(3)log_(3)5-1))>=&x-sqrt(x)-2>=0 is 0 (2) 1 (3) 2 (4) 3

Find the solution of the inequality 2log_(1/4)(x+5)>9/4log_(1/(3sqrt(3)))(9)+log_(sqrt(x+5))(2)

Find the solution of the inequality 2log_(1/4)(x+5)>9/4log_(1/(3sqrt(3)))(9)+log_(sqrt(x+5))(2)

Solve the following inequalities (i) log_(5)(3x-1) lt 1 (ii) (log_(.5)x)^(2)+log_(.5)x-2 le 0 (iii) log_(3)(x+1)+log_(3)(x+7) ge 3 (iv)log_(1//2)log_(3)(x^(2)+5)+1 le 0

Sum of integral values of x satisfying the inequality 3^((5/2)log_3(12-3x))-3^(log_3(x))>32