Use the properties of logarithms to evaluate each of the following expressions. (a) $4 \ln e^{2}+\ln e^{9}=$ (b) $\log _{2} 5-\log _{2} 20=$

Step 1 ：Use the properties of logarithms to evaluate each of the following expressions.

Step 2 ：For part (a), we can use the property of logarithms that states \(\ln e^{x} = x\). So, \(4 \ln e^{2}+\ln e^{9}\) simplifies to \(4*2 + 9\).

Step 3 ：For part (b), we can use the property of logarithms that states \(\log_{b} a - \log_{b} c = \log_{b} \frac{a}{c}\). So, \(\log _{2} 5-\log _{2} 20\) simplifies to \(\log_{2} \frac{5}{20}\), which is \(\log_{2} \frac{1}{4}\).

Step 4 ：Final Answer: (a) \(4 \ln e^{2}+\ln e^{9}= \boxed{17}\)

Step 5 ：Final Answer: (b) \(\log _{2} 5-\log _{2} 20= \boxed{-2}\)