Question

comparați numerele 5²² si 2⁵⁵ 5³³ si 3⁵⁵ 4³⁹ si 5²⁶ 4²² si 2⁴⁴ 2⁴⁴ si 5³³ 2⁴⁵ si 3³⁰ va rog frumos sa ma ajutati​

Answer 1

$\bf 5^{22} = \big(5^{2}\big)^{11} = 25^{11}$

$\bf 2^{55} = \big(2^{5}\big)^{11} = 32^{11}$

$\bf 25^{11}~<32^{11}\implies \blue{\underline{5^{22}~<~2^{22}}}$

                                                         

$\bf 5^{33} = \big(5^{3}\big)^{11} = 125^{11}$

$\bf 3^{55} = \big(3^{5}\big)^{11} = 243^{11}$

$\bf 125^{11}~<~243^{11}\implies \pink{\underline{5^{33}~<~3^{55}}}$

                                                         

$\bf 4^{39} = \big(4^{3}\big)^{13} = 64^{13}$

$\bf 5^{26} = \big(5^{2}\big)^{13} = 25^{13}$

$\bf 64^{13}~>~25^{13}\implies \green{\underline{4^{39}~>~5^{26}}}$

                                                         

$\bf 4^{22} = \big(2^{2}\big)^{11} = 4^{11}$

$\bf 2^{44} = \big(2^{4}\big)^{11} = 16^{11}$

$\bf 4^{11}~<~16^{11}\implies \green{\underline{4^{11}~<~2^{44}}}$

                                                         

$\bf 2^{44} = \big(2^{4}\big)^{11} = 16^{11}$

$\bf 5^{33} = \big(5^{3}\big)^{11} = 125^{11}$

$\bf 16^{11}~<~125^{11}\implies \red{\underline{2^{44}~<~5^{33}}}$

                                                         

$\bf 2^{45} = \big(2^{3}\big)^{15} = 8^{15}$

$\bf 3^{30} = \big(3^{2}\big)^{15} = 9^{15}$

$\bf 8^{15}~<~9^{15}\implies \purple{\underline{2^{45}~<~3^{30}}}$

$==pav38==$