Question

Помогите решить задачи, пжжжжжж!

Answer 1

Ответ:

95.

1)

${27}^{x} = 9 \\ {3}^{3x} = {3}^{2} \\ 3x = 2 \\ x = \frac{2}{3}$

2)

${ \frac{1}{5} }^{x} = 25 \\ {5}^{ - x} = {5}^{2} \\ - x = 2 \\ x = - 2$

3)

${4}^{x - 2} = 16 \\ {4}^{x - 2} = {4}^{2} \\ x - 2 = 2 \\ x = 2 + 2 \\ x = 4$

4)

${2}^{3x - 1} = \sqrt{2} \\ {2}^{3x - 1} = {2}^{ \frac{1}{2} } \\ 3x - 1 = \frac{1}{2} \\ 3x = \frac{1}{2} + 1 \\ 3x = \frac{3}{2} \\ x = \frac{3}{2} \div 3 \\ x = \frac{1}{2} = 0.5$

5)

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

6)

${3}^{ {x}^{2} + x - 12} = 1 \\ {3}^{ {x}^{2} + x - 12} = {3}^{0} \\ {x}^{2} + x - 12 = 0 \\ d = {b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times ( - 12) = 1 + 48 = 49 \\ x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 1 - \sqrt{49} }{2 \times 1} = \frac{ - 1 - 7}{2} = \frac{ - 8}{2} = - 4 \\ x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 1 + \sqrt{49} }{2 \times 1} = \frac{ - 1 + 7}{2} = \frac{ 6}{2} = 3$