If `x_1` and` x_2` are the solutions of the equation `x^(log_(10)x)=100x` such that `x_1gt1` and` x_2lt1`, the value of `(x_1x_2)/2`is

If x_1 and x_2 (x_2gtx_1) are the integral solutions of the equation (log_5x)^2+log_(5x)(5/x)=1 , , the value of |x_2-4x_1| is

The solution set of the equation sin ^(-1) x=2 tan ^(-1) x is

The solutions of the equation |(x,2,-1),(2,5,x),(-1,2,x)| =0 are

The solution set of the inequation (x^(2)+4 x+4)/(2 x^(2)-x-1) gt 0

Solve the inequation (x^(2)+x+1)^(x)lt1

x_(1) and x_(2) are two solutions of the equation e^(x) cos x=1 , The minimum number of the solution of the equation e^(x) sin x =1 , lying between x_(1) and x_(2) can be

The solution of the inequation (1-2 x-3 x^(2))/(3 x-x^(2)-5) gt 0 is

If x_1,x_2 & x_3 are the three real solutions of the equation x^(log_10^2 x+log_10 x^3+3)=2/((1/(sqrt(x+1)-1))-(1/(sqrt(x+1)+1))), where x_1 > x_2 > x_3, then these are in

Solve the following inequation . (xv) x^((log_10x)^2-3log_10x+1)gt1000

The number of solutions of the equation : x_2-x_3=1 -x_1+2x_3=2 x_1-2x_2=3 is :