[tex]\left\{ \begin{array}{c} 2^x = 5 \\ 5^y = 2 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x = log_\big25\\ y = log_\big52 \end{array} \right \Rightarrow \left\{ \begin{array}{c} x = log_\big25\\ y = \dfrac{log_\big22}{log_\big25} \end{array} \right \Rightarrow \left\{ \begin{array}{c} x = log_\big25\\ y = \dfrac{1}{log_\big25} \end{array} \right \Rightarrow [/tex]
[tex] \Rightarrow x\cdot y = log_\big25\cdot\dfrac{1}{log_\big25} \Rightarrow x\cdot y = \dfrac{log_\big25}{log_\big25}\Rightarrow \boxed{ x\cdot y = 1}[/tex]
[tex]$ \ $\Big( M-am folosit de formula de schimbare a bazei: log_\big{a}b= \dfrac{log_\big{c}b}{log_\big{c}a}$ $ \Big)[/tex]
