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Đáp án:
$15^{12} > 81^3.125^3$
$78^{12} - 78^{11} > 78^{11} - 78^{10}$
$21^{15} < 27^5.49^8$
$72^{45} - 72^{44} > 72^{44} - 72^{43}$
$125^5 > 25^7$
Giải thích các bước giải:
•
$15^{12} = (3.5)^{12} = 3^{12}.5^{12}$
$81^3.125^3 = (3^4)^3.(5^3)^3 = 3^{12}.5^9$
$=> 15^{12} > 81^3.125^3 (3^{12}.5^{12} > 3^{12}.5^9)$
•
$78^{12} - 78^{11} = 78^{11}.(78 - 1) = 78^{11}.77$
$78^{11} - 78^{10} = 78^{10}.(78 - 1) = 78^{10}.77$
$=> 78^{12} - 78^{11} > 78^{11} - 78^{10} (78^{11}.77 > 78^{10}.77)$
•
$21^{15} = (3.7)^{15} = 3^{15}.7^{15}$
$27^{5}.49^8 = (3^3)^5.(7^2)^8 = 3^{15}.7^{16}$
$=> 21^{15} < 27^5.49^8 (3^{15}.7^{15} < 3^{15}.7^{16})$
•
$72^{45} - 72^{44} = 72^{44}.(72 - 1) = 72^{44}.71$
$72^{44} - 72^{43} = 72^{43}.(72 - 1) = 72^{43}.71$
$=> 72^{45} - 72^{44} > 72^{44} - 72^{43} (72^{44}.71 > 72^{43}.71)$
•
$125^5 = (5^3)^5 = 5^{15}$
$25^7 = (5^2)^7 = 5^{14}$
$=> 125^5 > 25^7 (5^{15} > 5^{14})$
