Question

In ordine crescatoare:
a) 25 la puterea 18 , 125 la puterea15 si 5 la puterea 40;
b) 9 la puterea 51 , 27 la puterea 48 , 3 la puterea 95;
c) 8 la puterea 12, 32 la puterea 7, 27 la puterea 8



Rpd Pls !!!​

Answer 1

a) 25^18 = (5^2)^18 = 5^36

125^15 = (5^3)^15 = 5^45

5^36 < 5^40 < 5^45, adica 25^18 < 5^40 < 125^15

b) 9^51 = (3^2)^51 = 3^102

27^48 = (3^3)^48 = 3^144

3^95 < 3^102 < 3^144, adica 3^95 < 9^51 < 27^48

c) 8^12 = (2^3)^12 = 2^36

32^7 = (2^5)^7 = 2^35

2^35 < 2^36, adica 32^7 < 8^12

27^8 = (3^3)^8 = 3^24 = (3^2)^12 = 9^12

8^12 < 9^12, adica 8^12 < 27^8

Atunci 32^7 < 8^12 < 27^8