Răspuns:
[tex]1.\quad a) \; \red{2^{51}>2^{18}} \;\; b)\; \red{ 7^{32}<9^{32}}\\[/tex]
[tex]2.[/tex]
[tex]25^{\overline{ab}}<5^{26} \Rightarrow (5^2)^{\overline{ab}}<5^{26} \Rightarrow 5^{2\overline{ab}} <5^{26} \\\Rightarrow 2\overline{ab}=26\; \Big|:2 \Rightarrow \overline{ab} <13 \Rightarrow \red{\overline{ab} \in \{10,11,12\}}\\[/tex]
[tex]3.[/tex]
[tex]\left.\begin{aligned} 4^{32}=(2^2)^{32}=2^{32 \cdot 2}=2^{64}\;\; \\ 8^{24}=(2^3)^{24}=2^{3 \cdot 24}=2^{72}\;\; \\ 16^{25}=(2^4)^{25}=2^{4\cdot 25}=2^{100} \end{aligned} \right\} \Rightarrow \red{4^{32}<8^{24}<16^{25}} \\[/tex]
[tex]4.[/tex]
[tex]\left.\begin{aligned} 5^{72}=5^{3 \cdot 24} = (5^3)^{24}=125^{24} \\ 3^{96}=3^{4 \cdot 24}=(3^4)^{24}=81^{24}\; \end{aligned} \right\} \Rightarrow \red{ 5^{72}>3^{96}}[/tex]
