Una persona selecciona un número de dos algitos, luego resta este número a 200 y, finalmente, duplica el resultado. ¿Cuál es el mayor número que puede obtener mediante esta serie de operaciones?

Use the properties of logarithms to evaluate each of the following expressions. \( \begin{array}{l}\text { (a) } \ln e^{5}-8 \ln e^{2}=\square \\ \text { (b) } \log _{6} 18+\log _{6} 2=\square\end{array} \)

Use the properties of logarithms to evaluate each of the following expressions. \( \begin{array}{l}\text { (a) } 4 \ln e^{2}+\ln e^{-12}=\square \\ \text { (b) } \log _{3} 39-\log _{3} 13=\square\end{array} \)

Fill in the missing values to make the equations true. (a) \( \log _{4} 3-\log _{4} 7=\log _{4} \square \) (b) \( \log _{5} 7+\log _{5} \square=\log _{5} 42 \) (c) \( 2 \log _{9} 5=\log _{9} \square \)

7. Winnie wrote the following riddle: I am a number between 60 and 100 . My ones digit is two less than my tens digit. I am a prime number.

Let \( A=\{0,1,3\} \) and \( B=\{1,2,3,5,7\} \). Write \( R=\{(x, y) \mid x \in A, y \in B \wedge y=2 x+1\} \) in tabular form. Also find \( R^{-1} \)