Using Logarithm Properties Practice Test

Use the logarithm properties

<u>\log_b(xy)=\log_b(x)+\log_b(y),\quad \log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y),\quad \log_b(x^p)=p\log_b(x)</u>

to evaluate without a calculator: $$\log_3\left(\frac{81}{9}\right).$$

Use log properties to expand the expression: $$\log_2\left(\frac{(xy^2)^3}{\sqrt{z}}\right).$$