Question

кто поможет с решением

Answer 1

1)
${2}^{x} - {2}^{x - 2} = 24 \\ {2}^{ x - 2} ( {2}^{2} - 1) = 24 \\ {2}^{x - 2} \times 3 = 24 \\ {2}^{ x- 2} = 8 \\ {2}^{ x - 2} = {2}^{3} \\ x - 2 = 3 \\ x = 5$
${2}^{5 - 1} = {2}^{4} = 16$
Ответ: Г)

2)
${2}^{x + 1} - 7 \times {2}^{x - 2} = 16 \\ {2}^{x - 2} ( {2}^{3} - 7) = 16 \\ {2}^{x - 2} \times 1 = 16 \\ {2}^{x - 2} = 16 \\ {2}^{x - 2} = {2}^{4} \\ x - 2 = 4 \\ x = 6$
${2}^{6 - 1} = {2}^{5} = 32$
Ответ: Д)

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

4)
${2}^{x + 2} - {( \frac{1}{2} )}^{1 - x} = 56 \\ {2}^{ x + 2} - {2}^{x - 1} = 56 \\ {2}^{x - 1} ( {2}^{3} - 1) = 56 \\ {2}^{x - 1} \times 7 = 56 \\ {2}^{x - 1} = 8 \\ {2}^{x - 1 } = {2}^{3} \\ x - 1 = 3 \\ x = 4$
${2}^{4 - 1} = {2}^{3} = 8$
Ответ: В)