Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{\sqrt[3]{x^{4}}}{(x+7)^{5}}\right) \] Your answer should not have radicals or exponents. You may assume that all variables are positive.

Evaluate each expression. \[ \begin{array}{l}\text { (a) } \log _{7} \frac{1}{7}=\square \\ \text { (b) } \log _{3} 27=\square\end{array} \]

A town has a population of 16000 and grows at \( 4.5 \% \) every year. What will be the population after 8 years, to the nearest whole number?

Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{x^{3}}{\sqrt{(x+6)^{3}}}\right) \] Your answer should not have radicals or exponents. You may assume that all variables are positive. \( \log \left(\frac{x^{3}}{(x+6)^{3}}\right)=\square \)

de \( \frac{2}{3} \cdot\left(6-\frac{1}{4}\right) ? \)

Determine whether the following equation defines \( y \) as a function of \( x \) \[ x^{2}+y^{2}=121 \] Does the equation \( x^{2}+y^{2}=121 \) define \( y \) as a function of \( x \) ? Yes No No