Inecuatie logaritmica

[elena_romina]

Sa se determine x, y\( \in(0,1) \), stiind ca:

\( \log_{x} \frac{3xy}{2xy+x+y}+\log_{y}\frac{3xy}{2xy+x+y}+\log_{\frac{1}{2}}\frac{3xy}{2xy+x+y}\leq 3. \)

[Marius Mainea]

Se foloseste inegalitatea:

\( \log_a\frac{3abc}{ab+bc+ca}+\log_b\frac{3abc}{ab+bc+ca}+\log_c\frac{3abc}{ab+bc+ca}\ge 3 \)

\( a,b,c\in(0,1) \) cu egalitate daca si numai daca a=b=c.