Răspuns:
Explicație pas cu pas:
14a) 2n/21 = 6/7
6/7 se amplifica cu 3 => 18/21 = 2n/21 =>
2n = 18 => n = 18/2 => n = 9
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15a) x/2¹³ = 2¹⁵/4¹³ => x·4¹³ = 2¹⁵·2¹³ => x·(2²)¹³ = 2¹⁵⁺¹³ =>
x·2²ˣ¹³ = 2²⁸ => x = 2²⁸:2²⁶ => x = 2²⁸⁻²⁶ = 2² => x = 4
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16a) 2³¹/4²⁰ si 2²⁶/32⁷
2³¹/4²⁰ = 2³¹/(2²)²⁰ = 2³¹/2⁴⁰ = 2³¹⁻⁴⁰ = 2⁻⁹
2²⁶/32⁷ = 2²⁶/(2⁵)⁷ = 2²⁶/2⁵ˣ⁷ = 2²⁶/2³⁵ = 2²⁶⁻³⁵ = 2⁻⁹ =>
2³¹/4²⁰ = 2²⁶/32⁷ (fractiile sunt echivalente)
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17a) 2ⁿ/2¹⁰ = 2³³/2⁶ => 2ⁿ⁻¹⁰ = 2³³⁻⁶ =>
n-10 = 27 => n = 37
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18a) __ __
7/9 = x2/ 5x =>
7/9 = (10x+2)/(50+x) =>
7(50+x) = 9(10x+2) => 350+7x = 90x+18 =>
90x-7x = 350-18 => 83x = 332 =>
x = 332/83 => x = 4
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19a)
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ab / ba = 2/9 => (10a+b)/(10b+a) = 2/9 =>
9(10a+b) = 2(10b+a) => 90a+9b = 20b+2a =>
88a = 11b I:11 => 8a = b => b = 1 ; a = 8 =>
numarul este 81
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20a) 32⁵/2ⁿ⁺³ = 8ⁿ:4/16³ <=>
(2⁵)⁵/2ⁿ⁺³ = (2³)ⁿ:2²/(2⁴)³ <=>
2²⁵/2ⁿ⁺³ = 2³ⁿ⁻²/2¹² =>
2²⁵·2¹² = 2ⁿ⁺³·2³ⁿ⁻² => 2²⁵⁺¹² = 2ⁿ⁺³⁺³ⁿ⁻² =>
2³⁷ = 2⁴ⁿ⁺¹ => 4n+1 = 37 => n = 36/4 => n = 9
