Question

Comparați puterile:

13^15 ¦ 17^10
3^100¦ 2^150
5^4 ¦ 25^3
5^8 ¦ 125^3
9^4 ¦. 3^8​

Answer 1

Răspuns:

Bună!

1) $13^{15} > 17^{10}$

(13³)⁵ > ( 17²)⁵

2197⁵ > 289⁵

2) $3^{100} > 2^{150}$

(3⁴)²⁵ > (2⁶)²⁵

81²⁵ > 64²⁵

3) $5^{4} < 25^{3}$

5⁴ < 5⁶

4) $5^{8} < 125^{3}$

5⁸ < 5⁹

5) $9^{4} = 3^{8}$

3⁸ = 3⁸

Baftă!! (•ㅅ•)

Answer 2

Salutare !

(A)      $\bf 13^{15} > 17^{10}$

$\bf 13^{15} = (13^{3})^{5} = 2197^{5}$

$\bf 7^{15} = (7^{3})^{5} = 289^{5}$

(B)   $\bf 3^{100} > 2^{150}$

$\bf 3^{100} = (3^{4})^{25} = 81^{25}$

$\bf 2^{150} = (2^{6})^{25} = 64^{25}$

(C)  $\bf 5^{4} <25^{3}$

$\bf 25^{3} = (5^{2})^{3} = 5^{6}$

(D)   $\bf 5^{8} <125^{3}$

$\bf 125^{3} = (5^{3})^{3} = 5^{9}$

(E)  $\bf 9^{4} = 3^{8}$

$\bf 9^{4} = (3^{2})^{4} = 3^{8}$

==pav38==