Question

Ex:2,3
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Ajutor!

Answer 1

3.
a.
2^30=(2^3)^10=8^10
3^20=(3^2)^10=9^10

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

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

Answer 2

2.
a)2⁵³ si 4²⁹
   2⁵³ si (2²)²⁹
   2⁵³  <   2⁵⁸

b)9⁵¹ si 3¹⁰³
  (3²)⁵¹ si 3¹⁰³
   3¹⁰² < 3¹⁰³

c)4⁴⁷ si 8³¹
  (2²)⁴⁷ si (2³)³¹
  2⁹⁴ > 2⁹³

d)9²⁴ si 27¹⁶
  (3²)²⁴ si (3³)¹⁶
  3⁴⁸=3⁴⁸

e)125⁴³ si 25⁶¹
  (5³)⁴³ si (5²)⁶¹
   5¹²⁹ > 5¹²²

f)10⁴³ si 100¹⁹
  10⁴³ si (10²)¹⁹
  10⁴³ > 10³⁸

3.
a)2³⁰ si 3²⁰
30=3x10
20=2x10
(2³)¹⁰ si (3²)¹⁰
8¹⁰ < 9¹⁰ => 2³⁰ < 3²⁰

b)5³⁴ si 3⁵¹
34=2x17
51=3x17
(5²)¹⁷ si (3³)¹⁷
25¹⁷ < 27¹⁷ => 5³⁴ < 3⁵¹

c)2¹⁵⁵ si 3⁹³
155=5x31
93=3x31
(2⁵)³¹ si (3³)³¹
32³¹ > 27³¹ => 2¹⁵⁵ > 3⁹³

d)2¹¹¹·5³⁸ si 3¹³¹
111=3x37
38=2x19
131=1x131
(2³)⁷·(5²)¹⁹ si 3¹³¹
8⁷·25¹⁹ si 3¹³¹
25·8=200 =>2¹¹¹·5³⁸ > 3¹³¹

e)10⁷⁴ si 6¹²³
74=2x37
123=3x41
(10²)³⁷ si (6³)⁴¹
100³⁷ < 108⁴¹ (atat baza cat si exponentul primului termen sunt mai mici decat baza si exponentul celui de-al doilea termen)