Which of the following options correctly rewrites \( \log _{4}\left(\frac{9 m^{3}}{n}\right) \) using the Quotient Rule of Logarithms, the Product Rule of Logarithms, and the Power Rule of Logarithms? Option \#1: \( \log _{4} 9-3 \log _{4} m+\log _{4} n \) Option \#2: \( \log _{4} 9+3 \log _{4} m-\log _{4} n \) Option \#3: \( 3 \log _{4} 9 m-\log _{4} n \) (1 point)

1.Решить уравнение: \( \begin{array}{lll}\text { a) } \sqrt{x+3}=\sqrt{5-x} & \text { б) } \quad \sqrt{12+3 x}=2 & \text { в) } \quad x=1+\sqrt{x+11}\end{array} \)

Simplify the following expressions fully: \( 1.2 .1 \quad(x+2)\left(x^{2}-x+3\right) \)

Given that \( g(x)=\sqrt{\frac{2 x+3}{5 x+6}} \), find \( g^{-1}(x) \) \( g^{-1}(x)=x^{2}-3 x \)

Jika \( \left(\begin{array}{cc}-2 & 2 \\ 5 & y\end{array}\right)\left(\begin{array}{ll}5 & 3 \\ x & 4\end{array}\right)=\left(\begin{array}{cc}-6 & 2 \\ 27 & 19\end{array}\right) \), cari nilai \( x \) dan \( y \). If \( \left(\begin{array}{cc}-2 & 2 \\ 5 & y\end{array}\right)\left(\begin{array}{ll}5 & 3 \\ x & 4\end{array}\right)=\left(\begin{array}{cc}-6 & 2 \\ 27 & 19\end{array}\right) \), find the value of \( x \) and \( y \).

(12) If \( 4 n \geq 9 \), what is the least possible value of \( 4 n+1 ? \)