Question

AJUTATIMA SI PE MINE VA ROG E URGENT ​

Answer 1

Explicație pas cu pas:

15.a)4^31=(2^2)^31=2^62

8^21=(2^3)^21=2^63

16^15=(2^4)^15=2^60

Scris in oridine crescătoare: 16^15, 4^31, 8^21

b) 27^13=(3^3)^13=3^39

3^37=3^37(ramane asa cum este)

9^18=(3^2)^18=3^36

Scris in ordine crescatoare: 9^18, 3^37, 27^13

c)8^17=(2^3)^17=2^51

32^10=(2^5)^10=2^50

2^48=2^48

Scris in ordine crescatoare: 2^48, 32^10, 8^17

Answer 2

Răspuns:

Explicație pas cu pas:

15) a)  4³¹,  8²¹, 16¹⁵

4³¹ = ( 2²)³¹ = 2²ˣ³¹ = 2⁶²

8²¹ = ( 2³)²¹ = 2³ˣ²¹ = 2⁶³

16¹⁵ = ( 2⁴)¹⁵ = 2⁴ˣ¹⁵ = 2⁶⁰

=>    2⁶⁰ < 2⁶² < 2⁶³

=>    16¹⁵  <  4³¹ < 8²¹ ->   crescator

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b)   27¹³,   3³⁷, 9¹⁸

27¹³ = ( 3³)¹³ = 3³ˣ¹³ = 3³⁹

9¹⁸ = ( 3²)¹⁸ = 3²ˣ¹⁸ = 3³⁶

=>  3³⁶  <  3³⁷  < 3³⁹

=>    9¹⁸ <  3³⁷ < 27¹³

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c) 8¹⁷, 32¹⁰, 2⁴⁸

8¹⁷ = ( 2³)¹⁷ = 2³ˣ¹⁷ = 2⁵¹

32¹⁰ = ( 2⁵)¹⁰ = 2⁵ˣ¹⁰ = 2⁵⁰

=>   2⁴⁸ < 2⁵⁰ < 2⁵¹

=>   2⁴⁸ < 32¹⁰ < 8¹⁷

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d) 81¹¹,   9²¹, 3⁴¹

81¹¹ = ( 3⁴)¹¹ = 3⁴ˣ¹¹ = 3⁴⁴

9²¹ = ( 3²)²¹ = 3²ˣ²¹ = 3⁴²

=>   3⁴¹ < 3⁴² < 3⁴⁴

=>    3⁴¹ < 9²¹ <  81¹¹

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16) a)   2⁷⁵,  5³⁰, 3⁴⁵  ( Pentru a ordona aceste puteri cu baze si exponenti diferiti, aducem numerele la acelasi exponent, afland mai intai c.m.m.d.c al exponentilor:

75 = 5 x 15;   30 = 2 x 15;  45 = 3 x 15 =>  cmmdc = 15

2⁷⁵ = ( 2⁵)¹⁵ = 32¹⁵

5³⁰ = ( 5²)¹⁵ = 25¹⁵

3⁴⁵ = ( 3³)¹⁵ = 27¹⁵

=>   25¹⁵ < 27¹⁵ < 32¹⁵

=>    5³⁰ < 3⁴⁵  <  2⁷⁵

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b)    2⁹³, 7³¹,   3⁶²

2⁹³ = 2³ˣ³¹ = ( 2³)³¹ = 8³¹

3⁶² = 3²ˣ³¹ = ( 3²)³¹ = 9³¹

=>  7³¹  < 8³¹  <  9³¹

=>   7³¹ < 2⁹³ < 3⁶²

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c)    2⁷⁷,   11²²,  5³³

2⁷⁷ = 2⁷ˣ¹¹ = (2⁷)¹¹ = 128¹¹

11²² = 11²ˣ¹¹ = (11²)¹¹ = 121¹¹

5³³ = 5³ˣ¹¹ = ( 5³)¹¹ = 125¹¹

=>   121¹¹ <  125¹¹  <  128¹¹

=>   11²² <  5³³  <  2⁷⁷

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d)  2⁶⁹, 11²³,   3⁴⁶

69 = 3 x 23;  46 = 2 x 23

2⁶⁹ = 2³ˣ²³ = ( 2³)²³ = 8²³

3⁴⁶ = 3²ˣ²³ = ( 3²)²³ = 9²³

=>  8²³ < 9²³ < 11²³

=>    2⁶⁹  <   3⁴⁶  < 11²³

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17)

a)  

m = 2⁴¹ + 2⁴³

m = 2⁴¹ x ( 1 + 2²)

m = 2⁴¹ x 5

n = 2⁴⁴ - 2⁴¹

n = 2⁴¹ x ( 2³ - 1 )

n = 2⁴¹ x ( 8 - 1 )

n = 2⁴¹ x 7

=> 2⁴¹ x 5 < 2⁴¹ x 7  <=>     m < n

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b)  

m = 3²⁷ - 3²⁵ = 3²⁵ x ( 3² - 1 ) = 3²⁵ x 8

n = 3²⁵ + 3²⁶ = 3²⁵ x ( 1 + 3 ) = 3²⁵ x 4

=>   m > n, pentru ca:  3²⁵ x 8 > 3²⁵ x 4