Question Number 38099 by Cheyboy last updated on 21/Jun/18

Commented by MrW3 last updated on 22/Jun/18

Commented by MrW3 last updated on 22/Jun/18

Commented by prof Abdo imad last updated on 22/Jun/18
![(e)⇔e^(xlnx) =4^(−1) =e^(−ln(4)) =e^(−2ln(2)) ⇔xln(x)+2ln(2)=0 let f(x)=xln(x)+2ln(2) with x>0 f^′ (x)=ln(x) +1 ≥0 ⇔ln(x)≥ln((1/e)) ⇔x≥(1/e) so f is increasing on [(1/e),+∞[ and decreasing on]0,(1/e)] f((1/e))=−(1/e) +2ln(2)>0 lim_(x→0^+ ) f(x)=2ln(2)>0 lim_(x→+∞) f(x)=+∞ so f(x)≠0 ∀x>0 so the equation haven t any real solution.](https://www.tinkutara.com/question/Q38159.png)
Commented by Cheyboy last updated on 22/Jun/18

Commented by Cheyboy last updated on 22/Jun/18
