If a, b and c are positive numbers in a GP, then the roots of the quadratic equation `(log_e a)^2-(2log_e b)x+(log_ec)=0` are

If a, b and c are positive numbers in a G.P., then the roots of the quadratic equation (log_ea)x^2-(2log_eb)x.+(log_ec)=0 are

If a,b and c are positive numbers in a GP,then the roots of the quadratic equation (log_(e)a)^(2)-(2log_(e)b)x+(log_(e)c)=0 are

If a, b and c are positive numbers in a G.P., then the roots of the quadratic equation (log_(e ) a) x^(2) -(2 log_(e ) b) x + (log_(e ) C)=0 are

If a , b , c , are positive numbers in G.P . ,then the roots of the quadratic equation (log_(e)a)x^(2)-(2log_(e)b)x+(log_(e)c)=0

If the product of the roots of the quadratic equation x^(2)-5kx+3e^(log_(e)k)-1=0 be 8, then the value of k =

The number of real roots of equation log_e x+ ex=0

Let a,b" and "c are distinct positive numbers,none of them is equal to unity such that log _(b)a .log_(c)a+log_(a)b*log_(c)b+log_(a)c*log_(b)c-log_(b)a sqrt(a)*log_(sqrt(c))b^(1/3)*log_(a)c^(3)=0, then the value of abc is -

The number of real solution(s) of the equation 9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1 is equal to

The number of real solution(s) of the equation 9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1 is equal to