7) Use the Laws of Logarithms to combine the expression: \( 4 \log x-\frac{1}{3} \log \left(x^{2}+1\right)+2 \log (x-1) \)

3. Какое из данных равенств верно? \( \begin{array}{ll}\text { А) } 10^{-3}=-1000 & \text { В) }(-2)^{-3}=-\frac{1}{8} \\ \text { Б) }\left(-1 \frac{1}{3}\right)^{-2}=-\frac{9}{16} & \text { Г) } \frac{1}{7^{-2}}=-49\end{array} \)

Determine the vertical asymptotes and holes (removable points of discontinuity) of the rational function shown below. \[ f(x)=\frac{(x-8)(x-1)}{(x-1)(x+9)} \] Use commas to separate results if there are more than one of each. If there is not a hole or asymptote, record DNE as your answer. Holes \( x= \) \( x= \)

The logarithmic function \( \boldsymbol{y}=\log _{3}(\boldsymbol{x}-2) \) has a vertical asymptote at \( \boldsymbol{x}=\square \), an x-intercept at \( (\square, 0) \), and domain \( \square \)

Convert the complex number, \( z=2 \) cis \( \left(\frac{3 \pi}{2}\right) \), from polar to rectangular form. Enter your answer as \( a+b i \).

\( \frac{\sqrt{164+\sqrt{25}}}{\sqrt{140+\sqrt{16}}} \) işleminin sonucu kaçtır? \( \begin{array}{llll}\text { (A) } \frac{14}{13} & \text { B) } \frac{13}{12} & \text { C) } \frac{7}{6} & \text { D) } \frac{17}{12}\end{array} \)