Consider f(x) = x/lnx
Let x = e^y (since x > 0 this is a valid substitution)
f(y) = e^y/y
When y tending to 0- limit tends to - inf
When y tends to 0+ limit tends to +inf
f'(y) = 0 at y = 1 (single point) and value of f(y) at this coordinate is 'e' so it has only one extrema
At y = - inf
F(y) tends to zero
At y = +inf
f(y) tends to infinity
Hence we can easily plot this function now.
Can you see which values this function can't attain?
The answer should be [0,e)