로그 곱 계산

[출제의도] 계산능력-지수와 로그 $\log _{2} 3 + \log _{4} 9 = \log _{2} 3 + \log _{2 ^{2}} 3 ^{2} = \log _{2} 3 + \log _{2} 3 = 2 \log _{2} 3$ $\displaystyle \log _{3} 4 + \log _{9} 2 = \log _{3} 2 ^{2} + \log _{3 ^{2}} 2 = 2 \log _{3} 2 + \frac{1}{2} \log _{3} 2 = \frac{5}{2} \log _{3} 2$ 따라서 $\displaystyle \left( \log _{2} 3 + \log _{4} 9 \right) \left( \log _{3} 4 + \log _{9} 2 \right) = 2 \log _{2} 3 \times \frac{5}{2} \log _{3} 2 = 5$