Question

Укажите промежуток, содержащий корни уравнения
Помогите, пожалуйста!

Answer 1

$\log_{\sin \bigg {\frac{\pi}{4}} } (x^{2} - 5x + 8) = -4$

$\log_\bigg{\frac{\sqrt{2}}{2} } (x^{2} - 5x + 8) = -4$

$\log_\bigg{\frac{\sqrt{2}}{2} } (x^{2} - 5x + 8) = \log_\bigg{\frac{\sqrt{2}}{2} } \left( \dfrac{\sqrt{2}}{2} \right)^{-4}$

$\log_\bigg{\frac{\sqrt{2}}{2} } (x^{2} - 5x + 8) = \log_\bigg{\frac{\sqrt{2}}{2} } \left( \dfrac{2}{\sqrt{2}} \right)^{4}$

$\log_\bigg{\frac{\sqrt{2}}{2} } (x^{2} - 5x + 8) = \log_\bigg{\frac{\sqrt{2}}{2} } \left( \sqrt{2} \right)^{4}$

$\log_\bigg{\frac{\sqrt{2}}{2} } (x^{2} - 5x + 8) = \log_\bigg{\frac{\sqrt{2}}{2} } 4$

$x^{2} - 5x + 8 = 4$

$x^{2} - 5x + 4 = 0$

$\left\{\begin{array}{ccc}x_{1} + x_{2} = 5,\\x_{1}x_{2} = 4 \ \ \ \ \\\end{array}\right$

$x_{1} = 4\\x_{2} = 1$

Ответ: В) (0; 5).