Question

Puteți rezolva exercițiile de la 3 până la 9????
E urgent!!!!

Answer 1

^ in seamna la puterea
3.
a)
2^30 =(2^3)^10=8^10
3^20 =(3^2)^10=9^10
3^20 >2^30

b)
5^34 =(5^2)^17 =25^17
3^51=(3^3)^17=27^17
3^51 >5^34

c) 2^155 =(2^5)^31=32^31
  3^93=(3^3)^31=27^31
2^155 > 3^93

d) 2^111 × 5^38=(2^3)^37 x (5^2)^19 =8^37 × 25^19
3^131=(3^3)^19 × (3^2)^37 = 27^19 × 9^37
3^131 > 2^111 × 5^38

e) 10^74 =(10^2)^37 = 100^37
6^123 =(6^3)^41 =216^41
 10^74<6^123

4. 2^302= 2^300X2^2=(2^3)^100X4=8^100X4
3^203=3^200X3^3=(3^2)^100X27=9^100X27
3^203>2^302

5. 2^87+2^86+2^85=2^85*(2^2+2+1)=2^85 *7 =(2^5)^17 *7 =32^17*7
5^35+5^34=5^34(5+1)=(5^2)^17*6=25^17*6
2^87+2^86+2^85 >5^35+5^34

6. 3^(2n+1)-9^n =3^(2n+1)-3^2n =3^2n *(3-1) =3^2n*2
2(3n+1)-8^n=2(3n+1)-2^3n=2^3n(2-1)=2^3n
3^(2n+1)-9^n >2(3n+1)-8^n

7.  3^7 > 3^5
    2^3 <2^3+3^0
(3-5)^2 <3^2 * 5^2
(5^2)^3 = 5^12:5^6
(7^5)^2 =(7^4)^2 * 7^2

8. 2^2^3 = 2^8
   (2^2)^3=2^6      2^8>2^6

3^2^3=3^8
(3^2)^3=3^6    3^8>3^6

3^38=(3^2)^19 =9^19
2^59-2^58-2^57=2^57(2^2-2-1)=2^57 =(2^3) ^19=8^19
3^38>2^59

9^40=3^80
81^20=3^40
9^40=81^20

9. 2^2
   8=2^3
   4^2=2^4
   2^5
   2^7