посчитайте . в 1.1 во 2 :2,4,6,8,10,12

Question

Алгебра

Мартин

4 год назад

посчитайте . в 1.1 во 2 :2,4,6,8,10,12

ОТВЕТЫ

Костадин

Nov 29, 2020

1.

$1) {5}^{x - 4}= 625 \\{5}^{x - 4} ={5}^{4}\\ x - 4 = 4 \\ x = 8$

2.

$2) {3}^{x - 1}+{3}^{x + 1}= 30 \\{3}^{x - 1} (1 +{3}^{2} ) = 30 \\{3}^{ x - 1}\times 10 = 30 \\{?}^{x - 1}= 3 \\ x - 1 = 1 \\ x = 2$

$4) {7}^{x - 1}+ 3 \times{7}^{x}-{7}^{x - 2}= 153 \\{7}^{x - 2} (7 + 3 \times{7}^{2}- 1) = 153 \\{7}^{x - 2} (6 + 147) = 153 \\{7}^{x - 2}= 1 \\ x - 2 = 0 \\ x = 2$

$6) {7}^{x - 4}-{7}^{x - 3}=- 42 \\{7}^{x - 4} (1 - 7) =- 42 \\{7}^{x - 4}= 7 \\ x - 4 = 1 \\ x= 5$

$8) {5}^{x}+ 3 \times{5}^{x + 1}= 400 \\{5}^{x} (1 + 3 \times 5) = 400 \\{5}^{x} \times 16= 400 \\{5}^{x}= 25 \\ x = 2$

$10)3 \times{4}^{x}+{2}^{2x + 1} -{2}^{2x+ 5}=- 54\\ 3 \times{2}^{2x}+{2}^{2x + 1}-{2}^{2x + 5}=- 54 \\{2}^{2x} (3 + 2 -{2}^{5} ) =- 54 \\{2}^{2x}\times ( - 27) =- 54 \\{2}^{2x}= 2 \\ 2x = 1 \\ x = 0.5$

$12)15 \times{4}^{2 - x - 3 {x}^{2} }- 7 \times{4}^{3 - x - 3 {x}^{2} }+ 13 = 0 \\\\ 15 \times{4}^{2}\times{4}^{ - x - 3 {x}^{2} }- 7 \times{4}^{3}\times{4}^{ - x - 3 {x}^{2} }+ 13 = 0 \\{4}^{ - x - 3 {x}^{2} } (15 \times 16 - 7 \times 64) =- 13 \\{4}^{ - x - 3 {x}^{2} }\times ( - 208) =- 13 \\{4}^{ - x - 3 {x}^{2} }=\frac{1}{16 }\\{4}^{ -x - 3{x}^{2} }={4}^{ - 2}\\- x - 3 {x}^{2}=- 2 \\ 3 {x}^{2}+ x - 2 = 0 \\ D = 1 + 24 = 25 \\ x1 = ( - 1 + 5) \div 6 =\frac{2}{3}\\ x2 =- 1$

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