Use properties of logarithms to condense the logarithmic expression below. Write the expression as a single logarithm whose coefficient is 1 . Where possible, evaluate logarithmic expressions. \( 4 \ln x+3 \ln y-6 \ln z \) \( 4 \ln x+3 \ln y-6 \ln z=\square \)

Given the geometric sequence: \[ a_{1}=3, a_{2}=\frac{7}{3}, a_{3}=\frac{49}{27}, \ldots \] find a formula for the \( n \)-th term: \[ a_{n}=\square \]

Find the vertex of \( y=|x-9|+7 \) \[ \begin{array}{l}\text { a }(6,5) \\ \text { b }(7,3) \\ \text { c }(5,4) \\ \text { d }(9,7)\end{array} \]

8. \( 3^{3} \div 3+3-3(3) \)

Write the equation of the hyperbola \( 36 x^{2}-16 y^{2}+360 x-128 y+68=0 \) in standard form \[ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 \] Where: \( \mathrm{h}=\square \) \( \mathrm{k}=\square \) \( \mathrm{a}=\square \)

Let \( \ln 2=a, \ln 3=b \), and \( \ln 5=c \). Express the following logarithms in terms of \( a, b, c \) \( \ln 2000=\square \) \( \ln 0.192=\square \) \( \ln 0.054=\square \) \( \log _{2} 540=\square \)