QuestionБодлого 20. $6 \log _{x} 2-3 \log _{2} x+7=0$ тэгшитгэлийг бодно уу. A) $\left(8 ; \frac{\sqrt[3]{2}}{2}\right)$ B) 8 C) 3 D) $-\frac{2}{3}$

Studdy Solution
Convert back to $x$ using $y = \log_{2} x$:
For $y = 3$:
$$\log_{2} x = 3$$ $$x = 2^3 = 8$$
For $y = -\frac{2}{3}$:
$$\log_{2} x = -\frac{2}{3}$$ $$x = 2^{-\frac{2}{3}} = \frac{1}{2^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{4}} = \frac{\sqrt[3]{2}}{2}$$
The solutions for $x$ are:
A) $\left(8 ; \frac{\sqrt[3]{2}}{2}\right)$