посчитайте показательные уравнения

Question

Математика

Артём

6 год назад

посчитайте показательные уравнения

ОТВЕТЫ

Dimitrinka

Nov 26, 2020

$1) {2}^{ {x}^{2} - 5x + 6 }= 1 \\{x}^{2}- 5x + 6 = 0 \\ d = 25 - 24 = 1 \\ x1 = (5 + 1) \div 2 = 3 \\ x2 = 2$

: 2,3.

$2) {(0.4)}^{x - 1}={(6.25)}^{6x - 5 }\\\\{( \frac{2}{5}) }^{x - 1} ={( \frac{25}{4}) }^{6x - 5}\\{( \frac{2}{5} )}^{x - 1}={( \frac{2}{5}) }^{ - 2(6x - 5)}\\ x - 1 =- 12x + 10 \\ 13x = 11 \\ x =\frac{11}{13}$

$3) {5}^{2x - 1} ( {5}^{2}- 3) = 550 \\{5}^{2x - 1}\times 22 = 550 \\{5}^{2x - 1}= 25 \\ 2x - 1 = 2 \\ x = 1.5$

$4)2 \times{3}^{x - 1}-{3}^{x - 2}={5}^{x - 2}+ 4 \times{5}^{x - 3} \\{3}^{x - 2} (2 \times 3 - 1) ={5}^{x - 3} (5 + 4) \\{3}^{x - 2}\times 5 ={5}^{x - 3}\times 9 \\\frac{ {3}^{x - 2} }{ {5}^{x - 3} }=\frac{9}{5}\\\frac{ {3}^{x - 2} }{ {5}^{x - 3} }=\frac{3 \times 3}{5}\\\frac{ {3}^{x - 2} }{ {5}^{x - 3} \times 3 }=\frac{3}{5}\\\frac{ {3}^{x - 3} }{ {5}^{x - 3} }=\frac{3}{5}\\ x - 3 = 1 \\ x = 4$