Write the following as the sum and/or difference of logarithms. Assume all variables are positive. \( \log \left(\frac{6 y}{11}\right)= \) The answer format in lowercase characters is: \( \log \) (number) Spaces in the answer are optional.

If \( (2 a-5)(3 a-2)=6 a^{2}+k a+10 \), then \( k= \) \( \begin{array}{llll}\text { (a) } 15 & \text { (b) } 19 & \text { (c) }-19 & \text { (d) } 6\end{array} \)

Find the range of the quadratic function.

\( 4 \cdot 2^{-\frac{t}{5}}=288 \) Which of the following is the solution of the equation? Choose 1 answer: (A) \( t=-5 \log _{8}(288) \) (B) \( t=-5 \log _{72}(2) \) (C) \( t=-5 \log _{2}(72) \) (D) \( t=-5 \log _{288}(8) \)

\( \frac{(x-12)}{y}=18 \) where \( y=2 \)

\[ y=x^{2}+8 x+18 \] Write your answer as an inequality using \( x \) or \( y \) as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer