Question

Помогите решить 1 и 2 номера

Answer 1

1.

${5}^{ \frac{1}{ log_{4}x } } = 0.2 \\ {5}^{ \frac{1}{ log_{4}x } } = \frac{1}{5} \\ {5}^{ \frac{1}{ log_{4}x } } = {5}^{ - 1} \\ log_{4}x = - 1 \\ x = {4}^{ - 1} \\ x = \frac{1}{4}$

2.

${7}^{x} + {7}^{1 - x} = 8 \\ {7}^{x} + \frac{ {7}^{1} }{ {7}^{x} } = 8 \\ \frac{ {7}^{2x} + 7 - 8 \times {7}^{x} }{ {7}^{x} } = 0 \\ {7}^{2x} - 8 \times {7}^{x} + 7 = 0 \\ \\ {7}^{x} = a \\ \\ {a}^{2} - 8a + 7 = 0 \\ a _{1} +a _{2}= 8 \\ a _{1} \times a _{2}= 7 \\ a _{1} = 1 \\ a _{2}= 7$

${7}^{x} = 1 \\ {7}^{x} = {7}^{0} \\ x = 0 \\ \\ {7}^{x} = 7 \\ {7}^{x} = {7}^{1} \\ x = 1$

отрезок (0; 1)

Длина отрезка равна 1.

Ответ: 1