Question

Comparati numerele : 7 la puterea 21 si 5 la puterea 17 ; 3 la puterea 19 si 2 la puterea 13 ; 23 la puterea 41 si 41 la puterea 59.  VA ROG , AJUTATI-MA !!!!

Answer 1

Pentru a putea compara doua numere cu puteri, trebuie sa avem ori aceeasi baza, ori aceeasi putere

$7^{21}\ \ \ \ 5^{17}$

$7^{21}=(7^3)^7=343^7\\\\5^{17}=\frac{5^{21}}{5^4} =\frac{(5^3)^7}{5^4} =\frac{125^7}{5^4} \\\\343^7 > \frac{125^7}{5^4}$

$3^{19}\ \ \ \ 2^{13}$

$3^{19}=3^{13}\cdot 3^6\\\\2^{13} < 3^{13}$⇒

$3^{19} > 2^{13}$

$23^{41}\ \ \ \ 41^{59}$

$23^{41}\\\\41^{59}=41^{41}\cdot 4^{18}\\\\41^{41} > 23^{41}$⇒

$23^{41} < 41^{59}$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/228227

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