Question Number 116722 by ayenisamuel last updated on 06/Oct/20
$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:{e}^{{x}} −\mathrm{5}={k}\:{has}\:{no} \\ $$$${solution} \\ $$
Answered by Rio Michael last updated on 06/Oct/20
$${e}^{{x}} −\mathrm{5}\:=\:{k} \\ $$$$\Rightarrow\:{e}^{{x}} \:=\:{k}\:+\:\mathrm{5} \\ $$$${x}\:=\:\mathrm{ln}\:\left({k}\:+\:\mathrm{5}\right) \\ $$$$\mathrm{for}\:\mathrm{no}\:\mathrm{solution},\:\:{k}\:+\:\mathrm{5}\:\leqslant\:\mathrm{0}\:\Rightarrow\:{k}\:\leqslant\:−\mathrm{5} \\ $$