Question

Ordonati : 3 la puterea 100 , 5 la puterea 80 si 7 la puterea 60 . Crescator . Repede 34 pct.

Answer 1

100 = 2²· 5²
80= 2⁴ · 5
60 = 2² · 3·5 
-------------------------
cmmdc = 2²· 5 = 20 
3¹⁰⁰ = ( 3⁵ )²⁰ = 243 ²⁰ 
5⁸⁰ = ( 5⁴ ) ²⁰ = 625²⁰
7⁶⁰ =(7³ )²⁰ = 343²⁰ 
243  < 343 < 625 
atunci  243²⁰   < 343²⁰  < 625²⁰
3¹⁰⁰  < 7⁶⁰ < 5⁸⁰

Answer 2

na bun, x^y = x la puterea y, doar ca sa fim clari

3^100=3^(20*5)=(3^5)^20=243^20
5^80=5^(20*4)=(5^4)^20=625^20
7^60=7^(20*3)=(7^3)^20=343^20

243<343<625 => 243^20 < 343^20 < 625^20

deci 3^100 < 7^60 < 5^80