Question

1.Calculati cel mai mic nr nat , x pt care 3^ x+1 >27^12

2.Ordonati crescator nr: 2^61, 4,29, 8^20, 16^3

3. 4^301 >,<,= 2^61
3^17 >,<,= 9^8
25^11 >,<,= 5^23

DAU COROANA SI 50 puncte !!!!

Answer 1

1) 3ˣ⁺¹> (3³)¹² ⇒ 3ˣ⁺¹> 3³⁶⇒ x+1 >36⇒ x> 35⇒ x=36

2)
4²⁹ = (2²)²⁹ = 2⁵⁸
8²⁰ = (2³)²⁰ = 2⁶⁰
16³ =(2⁴)³ =2¹²
16³< 4²⁹ < 8²⁰ < 2⁶¹

3)
 4³⁰ (2⁶⁰) < 2⁶¹
3¹⁷ > 9⁸ (3¹⁶)
25¹¹ (5²²) < 5²³

Answer 2

1) 3^(x+1)>(3³)¹²
3^(x+1)>3³⁶
x+1=36
x=36-1
x=35, dar x>35=>x=36
2) Voi scrie toate numerele cu baza 2.
4²⁹=(2²)²⁹=2⁵⁸
8²⁰=(2³)²⁰=2⁶⁰
16³=(2⁴)³=2¹²
2¹²<2⁵⁸<2⁶⁰<2⁶¹; 16³<4²⁹<8²⁰<2⁶¹

3) (2²)³⁰... 2⁶¹
2⁶⁰<2⁶¹

3¹⁷...(3²)⁸
3¹⁷>3¹⁶

(5²)¹¹...5²³
5²²<5²³