Question

.............. розвязати

Answer 1

1)
${2}^{x} - {2}^{x - 2} = 24 \\ {2}^{x} - {2}^{x} \times {2}^{ - 2} = 24 \\ {2}^{x} - \frac{ {2}^{x} }{4} = 24 \\ 4 \times {2}^{x} - {2}^{x} = 96 \\ 3 \times {2}^{x} = 96 \\ {2}^{x} = 32 \\ {2}^{x} = {2}^{5} \\ x = 5$
Ответ: 5.

2)
${2}^{x + 1} - 7 \times {2}^{x - 2} = 16 \\ {2}^{x} \times 2 - 7 \times {2}^{x} \times {2}^{ - 2} = 16 \\ 2 \times {2}^{x} - \frac{7 \times {2}^{x} }{4} = 16 \\ 8 \times {2}^{x} - 7 \times {2}^{x} = 64 \\ {2}^{x} = 64 \\ {2}^{x} = {2}^{6} \\ x = 6$
Ответ: 6.

3)
${2}^{x + 4} - {( \frac{1}{2} )}^{ - x} = 120 \\ {2}^{x} \times {2}^{ 4} - {2}^{x} = 120 \\ 16 \times {2}^{x} - {2}^{x} = 120 \\ 15 \times {2}^{x} = 120 \\ {2}^{x} = 8 \\ {2}^{x} = {2}^{3} \\ x = 3$
Ответ: 3.

4)
${2}^{x + 2} - {( \frac{1}{2}) }^{1 - x} = 56 \\ {2}^{x + 2} - {2}^{x - 1} = 56 \\ {2}^{x} \times {2}^{2} - {2}^{x} \times {2}^{ - 1} = 56 \\ 4 \times {2}^{x} - \frac{ {2}^{x} }{2} = 56 \\ 8 \times {2}^{x} - {2}^{x} = 112 \\ 7 \times {2}^{x} = 112 \\ {2}^{x} = 16 \\ {2}^{x} = {2}^{4} \\ x = 4$
Ответ: 4