ACTIVITY 2: -Use the properties of logarithms to conde the expressions as a single logarithm. 1. \( \frac{2}{3} \operatorname{In} x-\frac{1}{2} \operatorname{In} y \) 2. \( 3 \log _{b} x+\log _{b}(2 x+1) \) 3. \( \log _{3}(9)+2 \)

a) \( \log \frac{27 \sqrt{10}}{3^{4} \sqrt{30}} \)

5. Use Structure Ms. Bush says each team will get more baseballs if there are 6 teams in the league. Mr. Rosin says each team will get more baseballs if there are 9 teams in the league. Who is correct? Compare by writing the symbol \( > \), \( < \), or \( = \). Tell how to decide without computing.

PREVIOUS ANSWERS ASK YOUR TEACHER Evaluate the square root, if possible, without using a calculator. (If the solution is not a real number, enter NOT REAL.) \( -\sqrt{-81} \)

1.3 The next term in the pattern \( 7 ; 1 ;-5 ;-11 \ldots \).... Will be _-_ A. 17 B. -17 C. -22 D. 16

Simplify the complex number \( i^{46} \) as much as possible.