Explain how you would use the Rational Root Theorem to test if \( \frac{1}{2} \) is a root of the polynomial \( 4x^{3} - 2x + 3 \).

Задание 2. Решить неравенства а) \( |3 x-3|>1 \) б) \( |x+3|<x-2 \) в) \( |3 x+2| \leq|5 x-4| \)

Which of the following is equivalent to \( 3 \ln a-\frac{1}{2}\left(\ln b+\ln c^{2}\right) ? \) (1 point) \( \frac{\ln \left(\frac{3 a}{0.5 b^{2} c}\right)}{\frac{3}{2} \ln \left(\frac{a}{b c^{2}}\right)} \) \( \ln \left(\frac{a^{3}}{b c^{2}}\right) \) \( \ln \left(\frac{a^{3}}{c \sqrt{b}}\right) \)

Solve \( \log _{2}\left(\log _{4} x\right)=3 \) (1 point) \[ \begin{array}{l}x=262,144 \\ x=4,096 \\ x=65,536 \\ x=6,561\end{array} \]

Rewrite the following as a single logarithmic expression: \( 3 \log _{b} m-2 \log _{b} n \) (1 point) \( \log _{b}\left(\frac{3 m}{2 n}\right) \) \( \log _{b}\left(m^{3} n^{2}\right) \) \( \log _{b}\left(\frac{m^{3}}{n^{2}}\right) \) \( \log _{b}\left(m^{3}-m^{2}\right) \)

1) \( \lg (x-1)-\lg (2 x-11)=\lg 2 \)