Răspuns :
[tex]x * y=2^{\ln x \cdot \ln y}[/tex]
a)
x*1=1
[tex]x * 1=2^{\ln x \cdot \ln 1}\\\\2^{\ln x \cdot \ln 1}=2^{lnx\cdot 0}=2^0=1[/tex]
b)
Elementul neutru
x*f=x
[tex]x * f=2^{\ln x \cdot \ln f}=x\ \ |logaritmam\\\\ln(2^{\ln x \cdot \ln f})=lnx\\\\lnx\cdot lnf\cdot ln2=lnx\\\\lnf\cdot ln2=1\\\\lnf=\frac{1}{ln2} \\\\f=e^{\frac{1}{ln2}}[/tex]
c)
[tex]x*\frac{1}{x} =2^{lnx\cdot ln\frac{1}{x}} \\\\2^{lnx\cdot ln\frac{1}{x}} =\frac{1}{2}\\\\ 2^{lnx\cdot ln\frac{1}{x}} =2^{-1}\\\\{lnx\cdot ln\frac{1}{x}}=-1\\\\lnx(ln1-lnx)=-1\\\\lnx(-lnx)=-1\\\\ln^2x=1\\\\lnx=1\\\\x=e\\\\sau\\\\lnx=-1\\\\x=e^{-1}[/tex]
Un alt exercitiu cu legi de compozitie gasesti aici: https://brainly.ro/tema/9905362
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