Question

срочно нужно решение, помогите пожалуйста, хотябы пеоловины

Answer 1

Ответ:

$7) {( \frac{5}{8} )}^{3x - 7} = {( \frac{8}{5} )}^{7x - 3} \\ { \frac{(5}{8} )}^{3x - 7} = {( \frac{5}{8}) }^{ - (7x - 3)} \\ 3x - 7 = - (7x - 3) \\ 3x - 7 = - 7x + 3 \\ 10x = 10 \\ x = 1$

$11) {3}^{2x} - 2 \times {3}^{x} - 3 = 0$

замена:

${3}^{x} = t$

${t}^{2} - 2t - 3 = 0 \\ d = 4 + 12 = 16 \\ t1 = (2 + 4) \div 2 = 3 \\ t2 = - 1$

${3}^{x} = 3 \\ x = 1 \\ {3}^{x} = - 1$

нет корней

Ответ: 1.

$9) {4}^{2x} - 3 \times {4}^{x} - 4 = 0$

замена:

${4}^{x} = t \\ {t}^{2} - 3t - 4 = 0 \\ d = 9 + 16 = 25 \\ t1 = (3 + 5) \div 2 = 4 \\ t2 = - 1$

${4}^{x} = 4 \\ x = 1 \\ {4}^{x} = - 1$

нет корней

Ответ: 1.

$17) {6}^{2x} + {6}^{ - 2x} = 2$

замена:

${6}^{2x} = t \\ t + \frac{1}{t} = 2 \\ {t}^{2} - 2t + 1 = 0 \\ {(t - 1)}^{2} = 0 \\ t = 1 \\ {6}^{2x} = 1 \\ 2x = 0 \\ x = 0$

$19) {3}^{ {x}^{2} - 3x} = {27}^{ {x}^{2} - 3x} \\ {3}^{ {x}^{2} - 3x} = {3}^{3( {x}^{2} - 3x)} \\ {x}^{2} - 3x = 3( {x}^{2} - 3x) \\ {x}^{2} - 3x - 3( {x}^{2} - 3x) = 0 \\ - 2( {x}^{2} - 3x) = 0 \\ x(x - 3) = 0 \\ x1 = 0 \\ x2 = 3$