If equation `log_(4)(2log_(3)(6+log_(2)(x^(2)+kx+9)))=1` has exactly two distinct real solutions,then least positive integral value of k,is

If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real roots, then the smallest integral value of |k| is:

If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solution for x, then possible integral value of a is:

Equation 2log_(8)(2x)+log_(8)(x^(2)+1-2x)=(4)/(3) has

Solve log_(2)(4xx3^(x)-6)-log_(2)(9^(x)-6)=1 .

The equation x^(3/4(log_(2)x)^(2)+log_(2)x-5/4)=sqrt(2) has

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

The equation log_(x^(2))16+log_(2x)64=3 has (a) one irrational solution (b) no prime solution two real solutions (d) no integral solution

The equation (log)_2(2x^2)+(log)_2xdotx^((log)_x((log)_2x+1))+1/2log4 2(x^4)+2^(-3(log)_(1/2)((log)_2x))=1 has exactly one real solution two real solutions three real solutions (d) no solution

If x^(4) + 2kx^(3) + x^(2) + 2kx + 1 = 0 has exactly tow distinct positive and two distinct negative roots, then find the possible real values of k.