Question

Aflati U cifra=a=6 la putere 123+3 la putere 146

Aratati can nr a=2 la putere 1 • 2 la putere 2 • 2 la putere 3 • 2 la putere 4...•2 la putere 40=

25 la putere x+3=125 la putere 8

Answer 1

a = 6^123 + 3^146

U(6^123) = 6

U ( 3^146) = U (3^2) = 9

U ( a) = U ( 6 + 9) = U ( 15) = 5
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a = 2^1 × 2^2 × 2^3 × 2^4 × ...× 2^40

(avem aceeasi baza si adunam exponentii )

a = 2 ^ ( 1 + 2 + 3 + 4 +...+ 40)

(calculam suma cu ajutorul Sumei lui Gauss)

a = 2^( 40 × 41 : 2)

a = 2^(20 × 41)

a = 2^820
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25^x+3 = 125^8

25^x × 25^3 = (5^3)^8

(5^2)^x × (5^2)^4 = 5^24

5^2x × 5^8 = 5^24

5^2x = 5^24 : 5^8

5^2x = 5^16

2x = 16

x = 8
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