Question

ex 1,2,3,4 dau coroana
1.comparati: a) 2⁵¹ cu 2¹⁸ b) 7³² cu 9³²
2.determinati nr nat. de forma ab, stiind ca 25ᵃᵇ<5²⁶
3.scrieti in ordine crescatoare nr. 4³², 8²⁴ si 16²⁵
4. comparati 5⁷² cu 3⁹⁶​

Answer 1

Răspuns:

$1.\quad a) \; \red{2^{51}>2^{18}} \;\; b)\; \red{ 7^{32}<9^{32}}$

$2.$

$25^{\overline{ab}}<5^{26} \Rightarrow (5^2)^{\overline{ab}}<5^{26} \Rightarrow 5^{2\overline{ab}} <5^{26} \\\Rightarrow 2\overline{ab}=26\; \Big|:2 \Rightarrow \overline{ab} <13 \Rightarrow \red{\overline{ab} \in \{10,11,12\}}$

$3.$

$\left.\begin{aligned} 4^{32}=(2^2)^{32}=2^{32 \cdot 2}=2^{64}\;\; \\ 8^{24}=(2^3)^{24}=2^{3 \cdot 24}=2^{72}\;\; \\ 16^{25}=(2^4)^{25}=2^{4\cdot 25}=2^{100} \end{aligned} \right\} \Rightarrow \red{4^{32}<8^{24}<16^{25}}$

$4.$

$\left.\begin{aligned} 5^{72}=5^{3 \cdot 24} = (5^3)^{24}=125^{24} \\ 3^{96}=3^{4 \cdot 24}=(3^4)^{24}=81^{24}\; \end{aligned} \right\} \Rightarrow \red{ 5^{72}>3^{96}}$