If `((log_(e)x)^(2)-3log_(e)x+3)/(log_(e)x-1)<1` then `x` belongs to

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

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

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

If x = 9 is one of the solutions of log_(e)(x^(2)+15a^(2))-log_(e)(a-2)=log_(e)((8ax)/(a-2)) ,then

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

int((log _(e)x)^(3))/(x)dx

int (dx)/(x(1+log_(e)x)(3+log_(e)x))

Draw the graph of y=log_(e)(-x),-log_(e)x,y=|log_(e)x|,y=log_(e)|x| and y=|log_(e)|x|| transforming the graph of y=log_(e)x.

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)