Use the properties of logarithms to evaluate each of the following expressions.
(a) $2 \log _{5} 3-\log _{5} 45=$
(b) $\quad \ln e^{9}+\ln e^{5}=$

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

Step 2 ：For the first question, we can use the properties of logarithms to simplify the expression. The properties we will use are: \(a \log_b c = \log_b c^a\) and \(\log_b a - \log_b c = \log_b \frac{a}{c}\)

Step 3 ：For the second question, we can use the property of natural logarithms that \(\ln e^a = a\)

Step 4 ：Calculate the value of the first expression: \(2 \log _{5} 3-\log _{5} 45\)

Step 5 ：The result of the first expression is \(-1.0\)

Step 6 ：Calculate the value of the second expression: \(\ln e^{9}+\ln e^{5}\)

Step 7 ：The result of the second expression is \(14.0\)

Step 8 ：Final Answer: \(2 \log _{5} 3-\log _{5} 45= \boxed{-1.0}\) and \(\ln e^{9}+\ln e^{5}= \boxed{14.0}\)