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