(log x)/(x)

f(x)=(x)/(ln x) and g(x)=(ln x)/(x). Then identify the CORRECT statement

y = (log x) ^ ((log x) ^ (log x) .... oo)

Prove that log_(ab)(x)=((log_(a)(x))(log_(b)(x)))/(log_(a)(x)+log_(b)(x))

Evaluate: int(ln(ln x))/(x ln x)dx,(x>0)

If x in(0,(pi)/(2))-{1,(pi)/(4)} then the expression (log_(cos x)(x)*log_(tan x)(x))/(log_(cos x)(x)+log_(tan x)(x)) simplifies to

Integrate the functions ,(1+x)(x+log x)^(2),((1+x)(x+log x)^(2))/(x)

lim_ (x rarr oo) (x ln (1+ (ln x) / (x))) / (ln x)

y The solution of the differential equation (dy)/(dx)=(x+y)/(x) satisfying the condition y(1)=1 is (1) y=ln x+x (2) quad y=x ln x+x^(2)y=x ln x+x^(2)y=x ln x+x

f(x) =log _x (log x) ,then f'(x) at x =eis

integrate (sqrt(1+ln x))/(x ln x)