17)
[tex]\it Fie \ k, \ elementul\ neutru.
\\ \\x*k=x \Rightarrow x^{2lnk} =x^1 \Rightarrow 2lnk=1 \Rightarrow lnk=\dfrac{1}{2} \Rightarrow k = e^{\frac{1}{2}} \Rightarrow k = \sqrt{e}[/tex]
18)
[tex]\it Fie\ x',\ simetricul\ lui\ x.
\\ \\
x*x'=k \Rightarrow x^{2lnx'} = e^{\frac{1}{2}} \Rightarrow ln x^{2lnx'} = ln e^{\frac{1}{2}} \Rightarrow 2lnx' lnx=\dfrac{1}{2} lne \Rightarrow
\\ \\ \\
\Rightarrow lnx'lnx=\dfrac{1}{4} \Rightarrow lnx' = \dfrac{1}{4lnx} \Rightarrow x'= e^{\frac{1}{4lnx}} [/tex]
