Find the possible values of `p` such that the equation `p x^2=(log)_e x` has exactly one solution.

Find the possible values of 'a' such that the inequality 3-x^(2)gt |x-a| has atleast one negative solution

Find the least value of k such that the equation (ln x) + k = e^(x-k) has a solution.

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

Find the values of p so that the equation 2cos^2x-(p+3)cosx+2(p-1)=0 has a real solution.

Find the values of p so that the equation 2cos^2x-(p+3)cosx+2(p-1)=0 has a real solution.

The equation 2log(x+3)=log(alphax) has only one solution if

Find the values of a if equation 1-cosx=(sqrt(3))/2|x|+ a ,x in (0,pi), has exactly one solution.

Find the values of a if equation 1-cosx=(sqrt(3))/2|x|+ a ,x in (0,pi), has exactly one solution.

Find the value of p for which the roots of the equation p x(x-2)+6=0, are equal.

Find the minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solutions.