Question

очень срочно помогите решить, дам 20 баллов
плииииз ​

Answer 1

Ответ:

1.

${125}^{x} = 0$

нет корней

2.

${( \frac{1}{4} )}^{x - 5} = \frac{1}{ \sqrt[8]{4} } \\ {4}^{ - (x - 5)} = {4}^{ - \frac{1}{8} } \\ - x + 5 = - \frac{1}{8} \\ - x = - \frac{41}{8} \\ x = \frac{41}{8}$

3.

${4}^{3x + 2} = {( \frac{1}{32} )}^{2x} \\ {2}^{2(3x + 2)} = {2}^{ - 5 \times 2x} \\ 6x + 4 = - 10x \\ 16x = - 4 \\ x = - 0.25$

4.

${5}^{0.25x - 5} = 625 \\ {5}^{0.25x - 5} = {5}^{4} \\ 0.25x - 5 = 4 \\ \frac{x} {4} = 9 \\ x = 36$

5.

${0.4}^{2x - 1} = 0.16 \\ {0.4}^{2x - 1} = {(0.4)}^{2} \\ 2x - 1 = 2 \\ 2x = 3 \\ x = 1.5$

6.

${17}^{x + 2.7} = \frac{1}{289} \\ {17}^{x + 2.7} = {17}^{ - 2} \\ x + 2.7 = - 2 \\ x = - 4.7$

7.

${0.09}^{2x - 9} = 0.0081 \\ {0.09}^{2x - 9} = {0.09}^{2} \\ 2x - 9 = 2 \\ 2x = 11 \\ x = 5.5$

8.

${( \frac{1}{25}) }^{2 - 16x} - 1 = 0 \\ {( \frac{1}{25} )}^{2 - 16x} = {( \frac{1}{25}) }^{0} \\ 2 - 16x = 0 \\ 16x = 2 \\ x = \frac{1}{8}$

9.

${( \frac{1}{5} )}^{x - 4} = 0.04 \\ {( \frac{1}{5}) }^{x - 4} = \frac{1}{25} \\ x - 4 = 2 \\ x = 6$

10.

${( \frac{2}{7}) }^{ 3x - 7 } = {3.5}^{x} \\ {3.5}^{ - (3x - 7)} = {3.5}^{x} \\ - 3x + 7 = x \\ - 4x = - 7 \\ x = \frac{7}{4}$

11.

${2.5}^{0.25x - 4} = {0.4}^{x - 121} \\ { (\frac{25}{10}) }^{0.25x - 4} = (\frac{4}{10} ) {}^{x - 121} \\ {( \frac{5}{2}) }^{0.25x - 4} = (\frac{2}{5} ) {}^{x - 121} \\ 0.25x - 4 = - x + 121 \\ 1.25x = 125 \\ x = 100$

12.

${(3 \frac{6}{25}) }^{ {x}^{2} - x - 1 } = {( \frac{5}{9} )}^{2x - 16} \\ {( \frac{81}{25}) }^{ {x}^{2} - x - 1 } = {( \frac{5}{9} )}^{2x - 16} \\ {( \frac{9}{5} )}^{2( {x}^{2} - x - 1)} = {( \frac{5}{9} )}^{2x - 16} \\ 2 {x}^{2} - 2x - 2 = - 2x + 16 \\ 2 {x}^{2} = 18 \\ {x}^{2} = 9 \\ x = \pm3$