[tex] x> 0 \\ log {}^{2} _{4}(x) - 3 log_{4}(x) = - 2 \\ log {}^{2} _{4}(x) - 3 log_{4}(x) + 2 = 0 \\ log_{4}(x) = a \\ {a}^{2} - 3a + 2 = 0 \\ {a}^{2} - a - 2a + 2 = 0 \\ a(a - 1) - 2(a - 1) = 0 \\ (a - 1)(a - 2) = 0 \\ a_{1} = 1 \\ a_{2} = 2 \\ \\ log_{4}(x) = 1 \\ log_{4}(x) = 2 \\ \\ log_{4}(x) = log_{4}(4) \\ log_{4}(x) = log_{4}(16) \\ \\ x_{1} = 4\\ x_{2} = 16[/tex]

Відповідь:

Пояснення: