Question

Решите пожалуйста .................

Answer 1

Вариант 3

1.

${3}^{x + 1} - 2 \times {3}^{x - 2} = 75 \\ ( {3}^{3} - 2) \times {3}^{x - 2} = 75 \\ (27 - 2) \times {3}^{x - 2} = 75 \\ 25 \times {3}^{x - 2} = 75 \\ {3}^{x - 2} = {3}^{1} \\ x - 2 = 1 \\ x = 1 + 2 \\ x = 3$

2.

$\sqrt{ {3}^{x} } = 9 \\ {3}^{ \frac{x}{2} } = {3}^{2} \\ \frac{x}{2} = 2 \\ x = 4$

Вариант 4

1.

${7}^{x - 2} = {4}^{2 - x} \\ x - 2 = 4 log_{7}(2) - 2 log_{7}(2) x \\ x + 2 log_{7}(2) x = 4 log_{7}(2) + 2 \\ (1 + 2 log_{7}(2) )x = 4 log_{7}(2) + 2 \\ x = \frac{2(2 log_{7}(2) + 1) }{1 + 2 log_{7}(2) } \\ x = 2$

2.

$\sqrt[3]{ {2}^{x} } = 8 \\ {2}^{ \frac{x}{3} } = {2}^{3} \\ \frac{x}{3} = 3 \\ x = 9$