Find the range of `f(x)=(log)_e x-((log)_e x)hat2)/(|(log)_e x)`

Explanation

`f(x)=log_(e)x-((log_(e)x)^(2))/(|log_(e)x|)`
`={(log_(e)x-((log_(e)x)^(2))/((log_(e)x))","log_(e)x gt 0),(log_(e)x-((log_(e)x)^(2))/((-log_(e)x))","log_(e)x lt 0):}`
`={(0", " x gt1),(2log_(e)x","0 lt x lt1):}`
Therefore, rnge is `(-oo,0]`.