Question

Чисто ответы не нужны, нужно с решением

Answer 1

Ответ:

1.

${2}^{3 - x} = 64 \\ {2}^{3 - x} = {2}^{6} \\ 3 - x = 6 \\ x = - 3$

2.

${2}^{x - 11} = \frac{1}{8} \\ {2}^{x - 11} = {2}^{ - 3} \\ x - 11 = - 3 \\ x = 8$

3.

${( \frac{1}{4}) }^{x - 4} = {( \frac{1}{4} )}^{3} \\ x - 4 = 3 \\ x = 7$

4.

${( \frac{1}{2}) }^{17 - 2x} = {( \frac{1}{2} )}^{ - 3} \\ 17 - 2x = - 3 \\ - 2x = - 20 \\ x = 10$

5.

${4}^{x - 1} = \frac{1}{2} \\ {4}^{x - 1} = {4}^{ - \frac{1}{2} } \\ x - 1 = - 0.5 \\ x = 0.5$

6.

${( \frac{1}{9}) }^{x - 9} = 3 \\ {3}^{ - 2(x - 9)} = 3 \\ - 2x + 18 = 3 \\ - 2x = - 16 \\ x = 8$

7.

${3}^{x + 1} = 3 \\ x + 1 = 1 \\ x = 0$

8.

${3}^{4 + 3x} = 0.6 \times {5}^{4 + 3x} \\ {3}^{4 + 3x} = \frac{3}{5} \times {5}^{4 + 3x} \\ \frac{ {3}^{4 + 3x} }{3} = \frac{ {5}^{4 + 3x} }{5} \\ {3}^{3x + 3} = {5}^{3x + 3} \\ \frac{ {3}^{3x + 3} }{ {5}^{3x + 3} } = 1 \\ 3x + 3 = 0 \\ x = - 1$

9.

${6}^{3 - 4x} = 0.36 \times {10}^{3 - 4x} \\ {6}^{3 - 4x} = \frac{36}{100} \times {10}^{3 - 4x} \\ {6}^{3 - 4x} \div {6}^{2} = {10}^{3 - 4x} \div {10}^{2} \\ {6}^{3 - 4x - 2} = {10}^{3 - 4x - 2} \\ {6}^{1 - 4x} = {10}^{1 - 4x} \\ 1 - 4x = 0 \\ x = \frac{1}{4} = 0.25$

10.

${25}^{x} - 4 \times {5}^{x} - 5 = 0$

пусть

${5}^{x} = t \\ {t}^{2} - 4 t - 5 = 0 \\ d = 16 + 20 = 36 \\ t1 = \frac{4 + 6}{2} = 5 \\ t2 = - 1 \\ \\ {5}^{x} = 5 \\ x = 1 \\ \\ {5}^{x} = - 1$

корней нет

Ответ: 1