Question

ex 1,va rog......................

Answer 1

   
[tex]\displaystyle\\ \sqrt[\b3]{3} \\ \log_3 2\\ \sqrt[\b4]{2} \\\\ \text{Explicatii:}\\ \sqrt[\b a]{b} \text{ si }\sqrt[\b c]{d}~~unde: ~~b,d \in R,~~a,c \in N \\ \text{Daca } b\ \textgreater \ 1,~d\ \textgreater \ 1, ~\text{ atunci }~ \sqrt[\b a]{b} \ \textgreater \ 1\text{ si }\sqrt[\b c]{d}\ \textgreater \ 1\\ \Longrightarrow~~\sqrt[\b3]{3} \ \textgreater \ 1\text{ si }\sqrt[\b4]{2} \ \textgreater \ 1\\\\ \text{Daca } b\ \textgreater \ d \text{ si } a\ \textless \ c,~\text{ atunci }~ \sqrt[\b a]{b} \ \textgreater \ \sqrt[\b c]{d}\\ \Longrightarrow~~\sqrt[\b3]{3} \ \textgreater \ \sqrt[\b4]{2}\\\\ \log_3 2 \ \textless \ \log_3 3 =1\\ \Longrightarrow~~\log_3 2 \ \textless \ 1\\\\ [/tex]

[tex]\displaystyle\\ \text{Ordonam crescator:}\\\\ \boxed{\log_3 2 \ \textless \ \sqrt[\b4]{2} \ \textless \ \sqrt[\b3]{3} }[/tex]