Question

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

Answer 1

Ответ:

1.

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

2.

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

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

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

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

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

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